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Math Problems
Grade 7
Solve two-step equations: word problems
Russell has been training for the Emerald Valley Race. The first week he trained, he ran
5
5
5
days and took the same two routes each day. He ran
2
2
2
miles around the football field before school and ran a longer route through his neighborhood after school. By the end of the week, Russell had run a total of
30
30
30
miles.
\newline
Which equation can Russell use to find how many miles,
x
x
x
, he ran each day after school?
\newline
Choices:
\newline
(A)
2
x
+
5
=
30
2x + 5 = 30
2
x
+
5
=
30
\newline
(B)
5
(
x
+
2
)
=
30
5(x + 2) = 30
5
(
x
+
2
)
=
30
\newline
(C)
2
(
x
+
5
)
=
30
2(x + 5) = 30
2
(
x
+
5
)
=
30
\newline
(D)
5
x
+
2
=
30
5x + 2 = 30
5
x
+
2
=
30
\newline
How many miles did Russell run each day after school?
\newline
Write your answer as a whole number or a simplified fraction.
\newline
____ miles
\newline
Get tutor help
Tanvi teaches art lessons at a day camp and needs to get supplies. She purchases
40
40
40
Bright Streak paint sets from the Color Splash art store. She uses a coupon she received in the mail for
10
$
10\$
10$
off her purchase. Tanvi spends
310
$
310\$
310$
in all.
\newline
Which equation can you use to find
p
p
p
, the original price of each Bright Streak paint set?
\newline
Choices:
\newline
(A)
10
(
p
−
40
)
=
310
10(p - 40) = 310
10
(
p
−
40
)
=
310
\newline
(B)
40
(
p
−
10
)
=
310
40(p - 10) = 310
40
(
p
−
10
)
=
310
\newline
(C)
40
p
−
10
=
310
40p - 10 = 310
40
p
−
10
=
310
\newline
(D)
10
p
−
40
=
310
10p - 40 = 310
10
p
−
40
=
310
\newline
What was the original price of each Bright Streak paint set?
\newline
____
$
\$
$
Get tutor help
Patty is ordering vests for her scout troop to wear in the Veterans Day parade. She ordered
12
12
12
vests from the Festive Features clothing shop. Since this was a bulk order, Festive Features reduced the price of each vest by
$
6
\$6
$6
. The total came to
$
132
\$132
$132
.
\newline
Which equation can you use to find the amount,
v
v
v
, Festive Features normally charges for a vest?
\newline
Choices:
\newline
(A)
6
(
v
−
12
)
=
132
6(v - 12) = 132
6
(
v
−
12
)
=
132
\newline
(B)
6
v
−
12
=
132
6v - 12 = 132
6
v
−
12
=
132
\newline
(C)
12
(
v
−
6
)
=
132
12(v - 6) = 132
12
(
v
−
6
)
=
132
\newline
(D)
12
v
−
6
=
132
12v - 6 = 132
12
v
−
6
=
132
\newline
How much does Festive Features normally charge for a vest?
\newline
____
$
\$
$
Get tutor help
Painted Pots lets customers choose and paint their own pottery. The store has teapots in multiple sizes. Rebecca chose to paint the largest teapot offered, which cost
18
$
18\$
18$
. She also painted
4
4
4
small teacups to go with her teapot. Rebecca spent a total of
42
$
42\$
42$
on pottery.
\newline
Which equation can you use to find
c
c
c
, the cost of each teacup?
\newline
Choices:
\newline
(A)
4
c
+
18
=
42
4c + 18 = 42
4
c
+
18
=
42
\newline
(B)
4
(
c
+
18
)
=
42
4(c + 18) = 42
4
(
c
+
18
)
=
42
\newline
(C)
18
c
+
4
=
42
18c + 4 = 42
18
c
+
4
=
42
\newline
(D)
18
(
c
+
4
)
=
42
18(c + 4) = 42
18
(
c
+
4
)
=
42
\newline
What was the cost of each teacup?
\newline
_
_
_
$
\_\_\_\$
___$
Get tutor help
Terrence signed up for the Safe Venture driving school. He will spend
10
10
10
hours driving with an instructor and will also attend weekly
2
2
2
-hour classes. When Terrence completes the
26
26
26
total hours of instruction, he will take his driver's test.
\newline
Which equation can you use to find
w
w
w
, the number of weeks the driving classes last?
\newline
Choices:
\newline
(A)
2
w
+
10
=
26
2w + 10 = 26
2
w
+
10
=
26
\newline
(B)
2
(
w
+
10
)
=
26
2(w + 10) = 26
2
(
w
+
10
)
=
26
\newline
(C)
10
(
w
+
2
)
=
26
10(w + 2) = 26
10
(
w
+
2
)
=
26
\newline
(D)
10
w
+
2
=
26
10w + 2 = 26
10
w
+
2
=
26
\newline
How many weeks do the driving classes last?
\newline
____ weeks
\newline
Get tutor help
Estelle is having her birthday party at Gold Frames Art Museum this year. A party package costs
265
$
265 \$
265$
and covers the entrance fee for guests, a private party room, and an activity guide. Estelle upgraded her package to include a favor for each of her
8
8
8
guests, bringing the total to
305
$
305 \$
305$
.
\newline
Which equation can you use to find
f
f
f
, the cost of each favor?
\newline
Choices:
\newline
(A)
8
f
+
265
=
305
8f + 265 = 305
8
f
+
265
=
305
\newline
(B)
265
(
f
+
8
)
=
305
265(f + 8) = 305
265
(
f
+
8
)
=
305
\newline
(C)
265
f
+
8
=
305
265f + 8 = 305
265
f
+
8
=
305
\newline
(D)
8
(
f
+
265
)
=
305
8(f + 265) = 305
8
(
f
+
265
)
=
305
\newline
How much did each favor cost?
\newline
_
_
_
_
$
\_\_\_\_ \$
____$
Get tutor help
Amy used her first
2
2
2
tokens at Glimmer Arcade to play a game of Roll-and-Score. Then she played her favorite game, Balloon Bouncer, over and over until she ran out of tokens. Balloon Bouncer costs
3
3
3
tokens per game, and Amy started with a bucket of
35
35
35
game tokens.
\newline
Which equation can Amy use to find how many games of Balloon Bouncer,
g
g
g
, she played?
\newline
Choices:
\newline
(A)
2
g
+
3
=
35
2g + 3 = 35
2
g
+
3
=
35
\newline
(B)
3
g
+
2
=
35
3g + 2 = 35
3
g
+
2
=
35
\newline
(C)
3
(
g
+
2
)
=
35
3(g + 2) = 35
3
(
g
+
2
)
=
35
\newline
(D)
2
(
g
+
3
)
=
35
2(g + 3) = 35
2
(
g
+
3
)
=
35
\newline
How many games of Balloon Bouncer did Amy play?
\newline
____ games
Get tutor help
Valentina is trying to decide whether to join her school's swim team. During the summer, the team practices
4
4
4
days per week. Each of those days, they practice for
3
3
3
hours in the morning and practice again in the afternoon. They practice for a total of
20
20
20
hours each week.
\newline
Which equation can you use to find
h
h
h
, the length of each afternoon practice in hours?
\newline
Choices:
\newline
(A)
4
(
h
+
3
)
=
20
4(h + 3) = 20
4
(
h
+
3
)
=
20
\newline
(B)
4
h
+
3
=
20
4h + 3 = 20
4
h
+
3
=
20
\newline
(C)
3
(
h
+
4
)
=
20
3(h + 4) = 20
3
(
h
+
4
)
=
20
\newline
(D)
3
h
+
4
=
20
3h + 4 = 20
3
h
+
4
=
20
\newline
How long is each afternoon practice?
\newline
Write your answer as a whole number or a simplified fraction.
\newline
____ hours
\newline
Get tutor help
Bert made
3
3
3
batches of his uncle's signature spicy wing sauce for a barbecue last weekend. He didn't want the sauce to be too spicy, so he tweaked the recipe, reducing the amount of hot sauce he put in each batch by
2
2
2
ounces. Bert used
24
24
24
ounces of hot sauce in all to make the wing sauce.
\newline
Which equation can you use to find
u
u
u
, the amount of hot sauce Bert's uncle usually puts in each batch of spicy wing sauce?
\newline
Choices:
\newline
(A)
3
u
−
2
=
24
3u - 2 = 24
3
u
−
2
=
24
\newline
(B)
2
u
−
3
=
24
2u - 3 = 24
2
u
−
3
=
24
\newline
(C)
3
(
u
−
2
)
=
24
3(u - 2) = 24
3
(
u
−
2
)
=
24
\newline
(D)
2
(
u
−
3
)
=
24
2(u - 3) = 24
2
(
u
−
3
)
=
24
\newline
How much hot sauce does Bert's uncle usually put in each batch of spicy wing sauce?
\newline
Write your answer as a whole number or a simplified fraction.
\newline
____ ounces
Get tutor help
Maplewood Furniture Store is having a sale on dining room furniture. When a customer purchases a set of dining chairs, a one-time discount of
55
55
55
$
\$
$
is applied to the total. During the sale, Rhianna buys a set of
6
6
6
chairs that match the table she inherited from her grandmother. Rhianna pays
455
455
455
$
\$
$
in all.
\newline
Which equation can you use to find the regular cost,
c
c
c
, of each chair?
\newline
Choices:
\newline
(A)
6
(
c
−
55
)
=
455
6(c - 55) = 455
6
(
c
−
55
)
=
455
\newline
(B)
55
c
−
6
=
455
55c - 6 = 455
55
c
−
6
=
455
\newline
(C)
6
c
−
55
=
455
6c - 55 = 455
6
c
−
55
=
455
\newline
(D)
55
(
c
−
6
)
=
455
55(c - 6) = 455
55
(
c
−
6
)
=
455
\newline
What is the regular cost of each chair?
\newline
____
$
\$
$
Get tutor help
Ms. Chapman wants to take her scout troop to Neon Nights roller rink. The employee she spoke to ahead of time said the total cost for all
9
9
9
people in the group would be
81
81
81
$
\$
$
. This includes an entrance ticket and a
3
3
3
$
\$
$
skate rental fee for each person. Which equation can you use to find
t
t
t
, the cost of each entrance ticket?
\newline
Choices:
\newline
(A)
9
t
+
3
=
81
9t + 3 = 81
9
t
+
3
=
81
\newline
(B)
3
t
+
9
=
81
3t + 9 = 81
3
t
+
9
=
81
\newline
(C)
9
(
t
+
3
)
=
81
9(t + 3) = 81
9
(
t
+
3
)
=
81
\newline
(D)
3
(
t
+
9
)
=
81
3(t + 9) = 81
3
(
t
+
9
)
=
81
\newline
How much does each entrance ticket cost?
\newline
____
$
\$
$
Get tutor help
Victor wants to learn to snowboard. He went to Snowy Ridge Mountain and rented a snowboard for
35
35
35
$
\$
$
, then took
5
5
5
hours of group snowboarding lessons. Victor paid
175
175
175
$
\$
$
in all.
\newline
Which equation can you use to find how much Snowy Ridge charges,
x
x
x
, for each hour of group snowboarding lessons?
\newline
Choices:
\newline
(A)
35
x
+
5
=
175
35x + 5 = 175
35
x
+
5
=
175
\newline
(B)
35
(
x
+
5
)
=
175
35(x + 5) = 175
35
(
x
+
5
)
=
175
\newline
(C)
5
x
+
35
=
175
5x + 35 = 175
5
x
+
35
=
175
\newline
(D)
5
(
x
+
35
)
=
175
5(x + 35) = 175
5
(
x
+
35
)
=
175
\newline
How much does Snowy Ridge charge for each hour of group snowboarding lessons?
\newline
____
$
\$
$
Get tutor help
Blue Tide Swim Shop is having its annual summer sale, when every item in the store gets marked down. During the sale, rashguards sell for
5
5
5
$
\$
$
less than full price. Miguel purchases
3
3
3
rashguards and pays a total of
60
60
60
$
\$
$
. Which equation can you use to find how much money,
f
f
f
, each rashguard costs at full price?
\newline
Choices:
\newline
(A)
3
(
f
−
5
)
=
60
3(f - 5) = 60
3
(
f
−
5
)
=
60
\newline
(B)
5
f
−
3
=
60
5f - 3 = 60
5
f
−
3
=
60
\newline
(C)
3
f
−
5
=
60
3f - 5 = 60
3
f
−
5
=
60
\newline
(D)
5
(
f
−
3
)
=
60
5(f - 3) = 60
5
(
f
−
3
)
=
60
\newline
How much does each rashguard cost at full price?
\newline
____
$
\$
$
Get tutor help
The Color Crate Exchange sends a new art activity in the mail each month. Nora prepaid a
6
6
6
-month subscription for her son. She signed up during their spring sale and received
12
12
12
$
\$
$
off the total cost. Nora paid
78
78
78
$
\$
$
in all.
\newline
Which equation can Nora use to find
m
m
m
, the regular cost per month?
\newline
Choices:
\newline
(A)
6
m
−
12
=
78
6m - 12 = 78
6
m
−
12
=
78
\newline
(B)
12
m
−
6
=
78
12m - 6 = 78
12
m
−
6
=
78
\newline
(C)
12
(
m
−
6
)
=
78
12(m - 6) = 78
12
(
m
−
6
)
=
78
\newline
(D)
6
(
m
−
12
)
=
78
6(m - 12) = 78
6
(
m
−
12
)
=
78
Get tutor help
At Trendy Tailor Boutique's annual end-of-season sale, every necktie in the shop gets marked down. Will purchased
7
7
7
neckties during the sale. Each necktie cost
8
8
8
$
\$
$
less than its full price. He paid a total of
147
147
147
$
\$
$
.
\newline
Which equation can you use to find
f
f
f
, the cost of each necktie at full price?
\newline
Choices:
\newline
(A)
7
f
−
8
=
147
7f - 8 = 147
7
f
−
8
=
147
\newline
(B)
7
(
f
−
8
)
=
147
7(f - 8) = 147
7
(
f
−
8
)
=
147
\newline
(C)
8
(
f
−
7
)
=
147
8(f - 7) = 147
8
(
f
−
7
)
=
147
\newline
(D)
8
f
−
7
=
147
8f - 7 = 147
8
f
−
7
=
147
Get tutor help
At the start of her shift at Midtown Bakery, Megan made some batches of cookies that called for
3
3
3
cups of flour each. Then, she used the remaining
8
8
8
cups of flour she had to make a pan of muffins. She started her shift with a
20
20
20
-cup bag of flour.
\newline
Which equation can you use to find how many batches of cookies,
x
x
x
, Megan made?
\newline
Choices:
\newline
(A)
8
(
x
+
3
)
=
20
8(x + 3) = 20
8
(
x
+
3
)
=
20
\newline
(B)
3
(
x
+
8
)
=
20
3(x + 8) = 20
3
(
x
+
8
)
=
20
\newline
(C)
8
x
+
3
=
20
8x + 3 = 20
8
x
+
3
=
20
\newline
(D)
3
x
+
8
=
20
3x + 8 = 20
3
x
+
8
=
20
\newline
How many batches of cookies did Megan make?
\newline
Write your answer as a whole number or a simplified fraction.
\newline
____ batches of cookies
\newline
Get tutor help
Painted Pots lets customers choose and paint their own pottery. The store has teapots in multiple sizes. Rebecca chose to paint the largest teapot offered, which cost
18
$
18\$
18$
. She also painted
4
4
4
small teacups to go with her teapot. Rebecca spent a total of
42
$
42\$
42$
on pottery.
\newline
Which equation can you use to find
c
c
c
, the cost of each teacup?
\newline
Choices:
\newline
(A)
4
(
c
+
18
)
=
42
4(c + 18) = 42
4
(
c
+
18
)
=
42
\newline
(B)
18
c
+
4
=
42
18c + 4 = 42
18
c
+
4
=
42
\newline
(C)
18
(
c
+
4
)
=
42
18(c + 4) = 42
18
(
c
+
4
)
=
42
\newline
(D)
4
c
+
18
=
42
4c + 18 = 42
4
c
+
18
=
42
\newline
What was the cost of each teacup?
\newline
_
_
_
$
\_\_\_\$
___$
Get tutor help
Ms. Chapman wants to take her scout troop to Neon Nights roller rink. The employee she spoke to ahead of time said the total cost for all
9
9
9
people in the group would be
$
81
\$81
$81
. This includes an entrance ticket and a
$
3
\$3
$3
skate rental fee for each person.
\newline
Which equation can you use to find
t
t
t
, the cost of each entrance ticket?
\newline
Choices:
\newline
(A)
9
(
t
+
3
)
=
81
9(t + 3) = 81
9
(
t
+
3
)
=
81
\newline
(B)
3
(
t
+
9
)
=
81
3(t + 9) = 81
3
(
t
+
9
)
=
81
\newline
(C)
3
t
+
9
=
81
3t + 9 = 81
3
t
+
9
=
81
\newline
(D)
9
t
+
3
=
81
9t + 3 = 81
9
t
+
3
=
81
\newline
How much does each entrance ticket cost?
\newline
____
$
\$
$
Get tutor help
Russell has been training for the Emerald Valley Race. The first week he trained, he ran
5
5
5
days and took the same two routes each day. He ran
2
2
2
miles around the football field before school and ran a longer route through his neighborhood after school. By the end of the week, Russell had run a total of
30
30
30
miles.
\newline
Which equation can Russell use to find how many miles,
x
x
x
, he ran each day after school?
\newline
Choices:
\newline
(A)
2
(
x
+
5
)
=
30
2(x + 5) = 30
2
(
x
+
5
)
=
30
\newline
(B)
5
(
x
+
2
)
=
30
5(x + 2) = 30
5
(
x
+
2
)
=
30
\newline
(C)
5
x
+
2
=
30
5x + 2 = 30
5
x
+
2
=
30
\newline
(D)
2
x
+
5
=
30
2x + 5 = 30
2
x
+
5
=
30
\newline
How many miles did Russell run each day after school?
\newline
Write your answer as a whole number or a simplified fraction.
\newline
____ miles
\newline
Get tutor help
The Oakland School's harvest festival is coming up, and Ms. Garza is in charge of ordering the caramel apples again. She knows she ordered
9
9
9
cases of caramel apples last year but can't remember how many apples come in a case. She checks last year's records and finds that the school sold
685
685
685
caramel apples and had
35
35
35
left over.
\newline
Which equation can Ms. Garza use to find how many caramel apples,
c
c
c
, come in each case?
\newline
Choices:
\newline
(A)
685
(
c
−
9
)
=
35
685(c - 9) = 35
685
(
c
−
9
)
=
35
\newline
(B)
9
c
−
685
=
35
9c - 685 = 35
9
c
−
685
=
35
\newline
(C)
685
c
−
9
=
35
685c - 9 = 35
685
c
−
9
=
35
\newline
(D)
9
(
c
−
685
)
=
35
9(c - 685) = 35
9
(
c
−
685
)
=
35
\newline
How many caramel apples come in each case?
\newline
____ caramel apples
\newline
Get tutor help
Amy used her first
2
2
2
tokens at Glimmer Arcade to play a game of Roll-and-Score. Then she played her favorite game, Balloon Bouncer, over and over until she ran out of tokens. Balloon Bouncer costs
3
3
3
tokens per game, and Amy started with a bucket of
35
35
35
game tokens.
\newline
Which equation can Amy use to find how many games of Balloon Bouncer,
g
g
g
, she played?
\newline
Choices:
\newline
(A)
2
g
+
3
=
35
2g + 3 = 35
2
g
+
3
=
35
\newline
(B)
3
(
g
+
2
)
=
35
3(g + 2) = 35
3
(
g
+
2
)
=
35
\newline
(C)
2
(
g
+
3
)
=
35
2(g + 3) = 35
2
(
g
+
3
)
=
35
\newline
(D)
3
g
+
2
=
35
3g + 2 = 35
3
g
+
2
=
35
\newline
How many games of Balloon Bouncer did Amy play?
\newline
____ games
Get tutor help
Terrence signed up for the Safe Venture driving school. He will spend
10
10
10
hours driving with an instructor and will also attend weekly
2
2
2
-hour classes. When Terrence completes the
26
26
26
total hours of instruction, he will take his driver's test.
\newline
Which equation can you use to find
w
w
w
, the number of weeks the driving classes last?
\newline
Choices:
\newline
(A)
10
(
w
+
2
)
=
26
10(w + 2) = 26
10
(
w
+
2
)
=
26
\newline
(B)
2
(
w
+
10
)
=
26
2(w + 10) = 26
2
(
w
+
10
)
=
26
\newline
(C)
2
w
+
10
=
26
2w + 10 = 26
2
w
+
10
=
26
\newline
(D)
10
w
+
2
=
26
10w + 2 = 26
10
w
+
2
=
26
\newline
How many weeks do the driving classes last?
\newline
____ weeks
Get tutor help
Valentina is trying to decide whether to join her school's swim team. During the summer, the team practices
4
4
4
days per week. Each of those days, they practice for
3
3
3
hours in the morning and practice again in the afternoon. They practice for a total of
20
20
20
hours each week.
\newline
Which equation can you use to find
h
h
h
, the length of each afternoon practice in hours?
\newline
Choices:
\newline
(A)
4
h
+
3
=
20
4h + 3 = 20
4
h
+
3
=
20
\newline
(B)
3
h
+
4
=
20
3h + 4 = 20
3
h
+
4
=
20
\newline
(C)
4
(
h
+
3
)
=
20
4(h + 3) = 20
4
(
h
+
3
)
=
20
\newline
(D)
3
(
h
+
4
)
=
20
3(h + 4) = 20
3
(
h
+
4
)
=
20
\newline
How long is each afternoon practice?
\newline
Write your answer as a whole number or a simplified fraction.
\newline
____ hours
\newline
Get tutor help
Genghis Motors wants to build cars and motorbikes on a budget. The company plans to spend at most
$
75000
\$75000
$75000
and use at least
320
320
320
workers to build cars and motorbikes.
\newline
8000
C
+
5500
M
≤
75000
8000C+5500M \leq 75000
8000
C
+
5500
M
≤
75000
represents the number of cars
C
C
C
and motorbikes
M
M
M
the company can build by spending at most
$
75000
\$75000
$75000
.
\newline
52
C
+
38
M
≥
320
52C+38M \geq 320
52
C
+
38
M
≥
320
represents the number of cars and motorbikes the company can build by using at least
320
320
320
workers.
\newline
Can the company meet both of its expectations by building
4
4
4
cars and
6
6
6
motorbikes?
\newline
Choose
1
1
1
answer:
\newline
(A) The company meets both of its expectations.
\newline
(B) The company uses the expected amount of money but not the expected number of workers.
\newline
(C) The company uses the expected number of workers but not the expected amount of money.
\newline
(D) The company doesn't meet either of its expectations.
Get tutor help
Fleur wants to make tables and chairs. She has a total of
150
150
150
wooden boards and
330
330
330
nails.
\newline
17
T
+
6
C
≤
150
17T+6C \leq 150
17
T
+
6
C
≤
150
represents the number of tables
T
T
T
and chairs
C
C
C
she can make with
150
150
150
wooden boards.
\newline
34
T
+
27
C
≤
330
34T+27C \leq 330
34
T
+
27
C
≤
330
represents the number of tables and chairs she can make with
330
330
330
nails.
\newline
Does Fleur have enough boards and nails to make
3
3
3
tables and
9
9
9
chairs?
\newline
Choose
1
1
1
answer:
\newline
(A) Fleur has enough boards and nails.
\newline
(B) Fleur has enough boards but not enough nails.
\newline
(C) Fleur has enough nails but not enough boards.
\newline
(D) Fleur has neither enough boards nor enough nails.
Get tutor help
Two cars are driving towards an intersection from perpendicular directions.
\newline
The first car's velocity is
10
10
10
meters per second and the second car's velocity is
6
6
6
meters per second.
\newline
At a certain instant, the first car is
4
4
4
meters from the intersection and the second car is
3
3
3
meters from the intersection.
\newline
What is the rate of change of the distance between the cars at that instant (in meters per second)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
136
-\sqrt{136}
−
136
\newline
(B)
−
5
-5
−
5
\newline
(C)
−
11.6
-\mathbf{1 1 . 6}
−
11.6
\newline
(D)
−
10
-10
−
10
.
8
8
8
Get tutor help
Two cars are driving towards an intersection from perpendicular directions.
\newline
The first car's velocity is
10
10
10
meters per second and the second car's velocity is
6
6
6
meters per second.
\newline
At a certain instant, the first car is
4
4
4
meters from the intersection and the second car is
3
3
3
meters from the intersection.
\newline
What is the rate of change of the distance between the cars at that instant (in meters per second)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
11
-11
−
11
.
6
6
6
\newline
(B)
−
10
-10
−
10
.
8
8
8
\newline
(C)
−
5
-5
−
5
\newline
(D)
−
136
-\sqrt{136}
−
136
Get tutor help
Two cars are driving towards an intersection from perpendicular directions.
\newline
The first car's velocity is
2
2
2
meters per second and the second car's velocity is
9
9
9
meters per second.
\newline
At a certain instant, the first car is
8
8
8
meters from the intersection and the second car is
6
6
6
meters from the intersection.
\newline
What is the rate of change of the distance between the cars at that instant (in meters per second)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
8
-8
−
8
.
4
4
4
\newline
(B)
−
7
-7
−
7
\newline
(C)
−
10
-10
−
10
\newline
(D)
−
85
-\sqrt{85}
−
85
Get tutor help
A grocery store sells four different jars of peanut butter. Determine which is the best buy, based on the cost per unit.
\newline
(A)
14
14
14
ounces for
$
1.51
\$ 1.51
$1.51
\newline
(B)
30
30
30
ounces for
$
3.54
\$ 3.54
$3.54
\newline
(C)
20
20
20
ounces for
$
1.88
\$ 1.88
$1.88
\newline
(D)
38
38
38
ounces for
$
4.37
\$ 4.37
$4.37
\newline
Which size jar is the best buy?
\newline
□
\square
□
ounces
Get tutor help
Jasina has a total of
$
0.80
\$ 0.80
$0.80
in nickels and dimes, and she has
4
4
4
more nickels than dimes. Which of the following systems of equations can be used to find out how many
n
n
n
nickels and
d
d
d
dimes she has?
\newline
Choose
1
1
1
answer:
\newline
(A)
d
+
n
=
4
0.1
d
+
0.05
n
=
0.8
d+n=4 \\ \quad 0.1 d+0.05 n=0.8
d
+
n
=
4
0.1
d
+
0.05
n
=
0.8
\newline
(B)
d
+
4
=
n
0.1
d
+
0.05
n
=
0.8
d+4=n \\ \quad 0.1 d+0.05 n=0.8
d
+
4
=
n
0.1
d
+
0.05
n
=
0.8
\newline
(C)
d
−
n
=
4
0.1
d
+
0.05
n
=
0.8
d-n=4 \\ \quad 0.1 d+0.05 n=0.8
d
−
n
=
4
0.1
d
+
0.05
n
=
0.8
\newline
(D)
n
−
d
=
−
4
0.1
d
+
0.05
n
=
0.8
n-d=-4 \\ \quad 0.1 d+0.05 n=0.8
n
−
d
=
−
4
0.1
d
+
0.05
n
=
0.8
Get tutor help
For a particular delivery, a courier travels by bicycle at a speed of
v
v
v
miles per hour for a distance of
1.3
1.3
1.3
miles. After making the delivery, the courier travels the same distance back, but travels
2
2
2
miles per hour faster than on the way to the delivery. If the courier spent
0.2
0.2
0.2
hours travelling to and from the delivery, which of the following equations could be used to determine the speed of the bicycle on the way to the delivery?
\newline
Choose
1
1
1
answer:
\newline
(A)
0.2
v
2
−
2.2
v
−
2.6
=
0
0.2v^{2}-2.2v-2.6=0
0.2
v
2
−
2.2
v
−
2.6
=
0
\newline
(B)
1.3
v
2
−
2
v
−
0.2
=
0
1.3v^{2}-2v-0.2=0
1.3
v
2
−
2
v
−
0.2
=
0
\newline
(C)
0.2
(
v
2
−
3
)
+
2.6
=
0
0.2(v^{2}-3)+2.6=0
0.2
(
v
2
−
3
)
+
2.6
=
0
\newline
(D)
3
(
0.2
−
v
)
(
2.6
−
v
)
=
0
3(0.2-v)(2.6-v)=0
3
(
0.2
−
v
)
(
2.6
−
v
)
=
0
Get tutor help
Victor wants to learn to snowboard. He went to Snowy Ridge Mountain and rented a snowboard for
35
35
35
$
\$
$
, then took
5
5
5
hours of group snowboarding lessons. Victor paid
175
175
175
$
\$
$
in all.
\newline
Which equation can you use to find how much Snowy Ridge charges,
x
x
x
, for each hour of group snowboarding lessons?
\newline
Choices:
\newline
(A)
35
(
x
+
5
)
=
175
35(x + 5) = 175
35
(
x
+
5
)
=
175
\newline
(B)
5
x
+
35
=
175
5x + 35 = 175
5
x
+
35
=
175
\newline
(C)
5
(
x
+
35
)
=
175
5(x + 35) = 175
5
(
x
+
35
)
=
175
\newline
(D)
35
x
+
5
=
175
35x + 5 = 175
35
x
+
5
=
175
\newline
How much does Snowy Ridge charge for each hour of group snowboarding lessons?
\newline
____
$
\$
$
Get tutor help
The Logan family is renting a beach house from Aqua Coast Beach Rentals. Mr. Logan called the rental agency ahead of time to get the total cost for
9
9
9
days. The rental agent explained that since the family plans to stay during the off-season, there will be a one-time discount of
25
25
25
$
\$
$
applied to their rental cost. The Logans will pay
920
920
920
$
\$
$
in all.
\newline
Which equation can you use to find
d
d
d
, how much the agency charges per day?
\newline
Choices:
\newline
(A)
9
(
d
−
25
)
=
920
9(d - 25) = 920
9
(
d
−
25
)
=
920
\newline
(B)
9
d
−
25
=
920
9d - 25 = 920
9
d
−
25
=
920
\newline
(C)
25
(
d
−
9
)
=
920
25(d - 9) = 920
25
(
d
−
9
)
=
920
\newline
(D)
25
d
−
9
=
920
25d - 9 = 920
25
d
−
9
=
920
\newline
How much does the agency charge per day?
\newline
____
$
\$
$
Get tutor help
The Logan family is renting a beach house from Aqua Coast Beach Rentals. Mr. Logan called the rental agency ahead of time to get the total cost for
9
9
9
days. The rental agent explained that since the family plans to stay during the off-season, there will be a one-time discount of
25
25
25
$
\$
$
applied to their rental cost. The Logans will pay
920
920
920
$
\$
$
in all.
\newline
Which equation can you use to find
d
d
d
, how much the agency charges per day?
\newline
Choices:
\newline
(
A
)
25
(
d
−
9
)
=
920
(A) 25(d - 9) = 920
(
A
)
25
(
d
−
9
)
=
920
\newline
(
B
)
25
d
−
9
=
920
(B) 25d - 9 = 920
(
B
)
25
d
−
9
=
920
\newline
(
C
)
9
d
−
25
=
920
(C) 9d - 25 = 920
(
C
)
9
d
−
25
=
920
\newline
(
D
)
9
(
d
−
25
)
=
920
(D) 9(d - 25) = 920
(
D
)
9
(
d
−
25
)
=
920
\newline
How much does the agency charge per day?
\newline
____
$
\$
$
Get tutor help
Estelle is having her birthday party at Gold Frames Art Museum this year. A party package costs
265
265
265
$
\$
$
and covers the entrance fee for guests, a private party room, and an activity guide. Estelle upgraded her package to include a favor for each of her
8
8
8
guests, bringing the total to
305
305
305
$
\$
$
.
\newline
Which equation can you use to find
f
f
f
, the cost of each favor?
\newline
Choices:
\newline
(A)
265
(
f
+
8
)
=
305
265(f + 8) = 305
265
(
f
+
8
)
=
305
\newline
(B)
265
f
+
8
=
305
265f + 8 = 305
265
f
+
8
=
305
\newline
(C)
8
(
f
+
265
)
=
305
8(f + 265) = 305
8
(
f
+
265
)
=
305
\newline
(D)
8
f
+
265
=
305
8f + 265 = 305
8
f
+
265
=
305
\newline
How much did each favor cost?
\newline
____
$
\$
$
Get tutor help
The Logan family is renting a beach house from Aqua Coast Beach Rentals. Mr. Logan called the rental agency ahead of time to get the total cost for
9
9
9
days. The rental agent explained that since the family plans to stay during the off-season, there will be a one-time discount of
25
25
25
$
\$
$
applied to their rental cost. The Logans will pay
920
920
920
$
\$
$
in all.
\newline
Which equation can you use to find
d
d
d
, how much the agency charges per day?
\newline
Choices:
\newline
(
A
)
9
(
d
−
25
)
=
920
(A) 9(d - 25) = 920
(
A
)
9
(
d
−
25
)
=
920
\newline
(
B
)
25
(
d
−
9
)
=
920
(B) 25(d - 9) = 920
(
B
)
25
(
d
−
9
)
=
920
\newline
(
C
)
9
d
−
25
=
920
(C) 9d - 25 = 920
(
C
)
9
d
−
25
=
920
\newline
(
D
)
25
d
−
9
=
920
(D) 25d - 9 = 920
(
D
)
25
d
−
9
=
920
\newline
How much does the agency charge per day?
\newline
____
$
\$
$
Get tutor help
Victor wants to learn to snowboard. He went to Snowy Ridge Mountain and rented a snowboard for
35
35
35
$
\$
$
, then took
5
5
5
hours of group snowboarding lessons. Victor paid
175
175
175
$
\$
$
in all.
\newline
Which equation can you use to find how much Snowy Ridge charges,
x
x
x
, for each hour of group snowboarding lessons?
\newline
Choices:
\newline
(A)
35
x
+
5
=
175
35x + 5 = 175
35
x
+
5
=
175
\newline
(B)
5
(
x
+
35
)
=
175
5(x + 35) = 175
5
(
x
+
35
)
=
175
\newline
(C)
35
(
x
+
5
)
=
175
35(x + 5) = 175
35
(
x
+
5
)
=
175
\newline
(D)
5
x
+
35
=
175
5x + 35 = 175
5
x
+
35
=
175
\newline
How much does Snowy Ridge charge for each hour of group snowboarding lessons?
\newline
____
$
\$
$
Get tutor help
Estelle is having her birthday party at Gold Frames Art Museum this year. A party package costs
265
265
265
$
\$
$
and covers the entrance fee for guests, a private party room, and an activity guide. Estelle upgraded her package to include a favor for each of her
8
8
8
guests, bringing the total to
305
305
305
$
\$
$
.
\newline
Which equation can you use to find
f
f
f
, the cost of each favor?
\newline
Choices:
\newline
(A)
265
(
f
+
8
)
=
305
265(f + 8) = 305
265
(
f
+
8
)
=
305
\newline
(B)
8
f
+
265
=
305
8f + 265 = 305
8
f
+
265
=
305
\newline
(C)
265
f
+
8
=
305
265f + 8 = 305
265
f
+
8
=
305
\newline
(D)
8
(
f
+
265
)
=
305
8(f + 265) = 305
8
(
f
+
265
)
=
305
\newline
How much did each favor cost?
\newline
____
$
\$
$
Get tutor help
Victor wants to learn to snowboard. He went to Snowy Ridge Mountain and rented a snowboard for
35
35
35
$
\$
$
, then took
5
5
5
hours of group snowboarding lessons. Victor paid
175
175
175
$
\$
$
in all.
\newline
Which equation can you use to find how much Snowy Ridge charges,
x
x
x
, for each hour of group snowboarding lessons?
\newline
Choices:
\newline
(A)
5
(
x
+
35
)
=
175
5(x + 35) = 175
5
(
x
+
35
)
=
175
\newline
(B)
5
x
+
35
=
175
5x + 35 = 175
5
x
+
35
=
175
\newline
(C)
35
(
x
+
5
)
=
175
35(x + 5) = 175
35
(
x
+
5
)
=
175
\newline
(D)
35
x
+
5
=
175
35x + 5 = 175
35
x
+
5
=
175
\newline
How much does Snowy Ridge charge for each hour of group snowboarding lessons?
\newline
____
$
\$
$
Get tutor help
Victor wants to learn to snowboard. He went to Snowy Ridge Mountain and rented a snowboard for
35
35
35
$
\$
$
, then took
5
5
5
hours of group snowboarding lessons. Victor paid
175
175
175
$
\$
$
in all.
\newline
Which equation can you use to find how much Snowy Ridge charges,
x
x
x
, for each hour of group snowboarding lessons?
\newline
Choices:
\newline
(A)
35
(
x
+
5
)
=
175
35(x + 5) = 175
35
(
x
+
5
)
=
175
\newline
(B)
5
(
x
+
35
)
=
175
5(x + 35) = 175
5
(
x
+
35
)
=
175
\newline
(C)
35
x
+
5
=
175
35x + 5 = 175
35
x
+
5
=
175
\newline
(D)
5
x
+
35
=
175
5x + 35 = 175
5
x
+
35
=
175
\newline
How much does Snowy Ridge charge for each hour of group snowboarding lessons?
\newline
____
$
\$
$
Get tutor help
Estelle is having her birthday party at Gold Frames Art Museum this year. A party package costs
265
265
265
$
\$
$
and covers the entrance fee for guests, a private party room, and an activity guide. Estelle upgraded her package to include a favor for each of her
8
8
8
guests, bringing the total to
305
305
305
$
\$
$
.
\newline
Which equation can you use to find
f
f
f
, the cost of each favor?
\newline
Choices:
\newline
(A)
265
f
+
8
=
305
265f + 8 = 305
265
f
+
8
=
305
\newline
(B)
265
(
f
+
8
)
=
305
265(f + 8) = 305
265
(
f
+
8
)
=
305
\newline
(C)
8
f
+
265
=
305
8f + 265 = 305
8
f
+
265
=
305
\newline
(D)
8
(
f
+
265
)
=
305
8(f + 265) = 305
8
(
f
+
265
)
=
305
\newline
How much did each favor cost?
\newline
____
$
\$
$
Get tutor help
The Logan family is renting a beach house from Aqua Coast Beach Rentals. Mr. Logan called the rental agency ahead of time to get the total cost for
9
9
9
days. The rental agent explained that since the family plans to stay during the off-season, there will be a one-time discount of
25
25
25
$
\$
$
applied to their rental cost. The Logans will pay
920
920
920
$
\$
$
in all.
\newline
Which equation can you use to find
d
d
d
, how much the agency charges per day?
\newline
Choices:
\newline
(A)
25
d
−
9
=
920
25d - 9 = 920
25
d
−
9
=
920
\newline
(B)
9
d
−
25
=
920
9d - 25 = 920
9
d
−
25
=
920
\newline
(C)
25
(
d
−
9
)
=
920
25(d - 9) = 920
25
(
d
−
9
)
=
920
\newline
(D)
9
(
d
−
25
)
=
920
9(d - 25) = 920
9
(
d
−
25
)
=
920
\newline
How much does the agency charge per day?
\newline
____
$
\$
$
Get tutor help
Victor wants to learn to snowboard. He went to Snowy Ridge Mountain and rented a snowboard for
35
35
35
$
\$
$
, then took
5
5
5
hours of group snowboarding lessons. Victor paid
175
175
175
$
\$
$
in all.
\newline
Which equation can you use to find how much Snowy Ridge charges,
x
x
x
, for each hour of group snowboarding lessons?
\newline
Choices:
\newline
(A)
35
(
x
+
5
)
=
175
35(x + 5) = 175
35
(
x
+
5
)
=
175
\newline
(B)
35
x
+
5
=
175
35x + 5 = 175
35
x
+
5
=
175
\newline
(C)
5
(
x
+
35
)
=
175
5(x + 35) = 175
5
(
x
+
35
)
=
175
\newline
(D)
5
x
+
35
=
175
5x + 35 = 175
5
x
+
35
=
175
\newline
How much does Snowy Ridge charge for each hour of group snowboarding lessons?
\newline
____
$
\$
$
Get tutor help
The Logan family is renting a beach house from Aqua Coast Beach Rentals. Mr. Logan called the rental agency ahead of time to get the total cost for
9
9
9
days. The rental agent explained that since the family plans to stay during the off-season, there will be a one-time discount of
25
25
25
$
\$
$
applied to their rental cost. The Logans will pay
920
920
920
$
\$
$
in all.
\newline
Which equation can you use to find
d
d
d
, how much the agency charges per day?
\newline
Choices:
\newline
(
A
)
9
d
−
25
=
920
(A) 9d - 25 = 920
(
A
)
9
d
−
25
=
920
\newline
(
B
)
9
(
d
−
25
)
=
920
(B) 9(d - 25) = 920
(
B
)
9
(
d
−
25
)
=
920
\newline
(
C
)
25
d
−
9
=
920
(C) 25d - 9 = 920
(
C
)
25
d
−
9
=
920
\newline
(
D
)
25
(
d
−
9
)
=
920
(D) 25(d - 9) = 920
(
D
)
25
(
d
−
9
)
=
920
\newline
How much does the agency charge per day?
\newline
____
$
\$
$
Get tutor help
Valentina is trying to decide whether to join her school's swim team. During the summer, the team practices
4
4
4
days per week. Each of those days, they practice for
3
3
3
hours in the morning and practice again in the afternoon. They practice for a total of
20
20
20
hours each week.
\newline
Which equation can you use to find
h
h
h
, the length of each afternoon practice in hours?
\newline
Choices:
\newline
(A)
3
h
+
4
=
20
3h + 4 = 20
3
h
+
4
=
20
\newline
(B)
4
h
+
3
=
20
4h + 3 = 20
4
h
+
3
=
20
\newline
(C)
4
(
h
+
3
)
=
20
4(h + 3) = 20
4
(
h
+
3
)
=
20
\newline
(D)
3
(
h
+
4
)
=
20
3(h + 4) = 20
3
(
h
+
4
)
=
20
\newline
How long is each afternoon practice?
\newline
Write your answer as a whole number or a simplified fraction.
\newline
____ hours
\newline
Get tutor help
Lester is on the well-known reality show, Kid Castaway, in which a group of kids spends a week learning to survive on a tropical island. On Monday, the kids gather a bunch of coconuts to eat. They divide the coconuts evenly among all
18
18
18
kids in the group. Each kid gets
4
4
4
coconuts.
\newline
Which equation can you use to find the number of coconuts
c
c
c
the kids gather?
\newline
Choices:
\newline
(A)
18
c
=
4
18c = 4
18
c
=
4
\newline
(B)
c
18
=
4
\frac{c}{18} = 4
18
c
=
4
\newline
(C)
c
+
18
=
4
c + 18 = 4
c
+
18
=
4
\newline
(D)
c
−
18
=
4
c - 18 = 4
c
−
18
=
4
\newline
Solve this equation for
c
c
c
to find the number of coconuts the kids gather.
\newline
____ coconuts
\newline
Get tutor help
Amy used her first
2
2
2
tokens at Glimmer Arcade to play a game of Roll-and-Score. Then she played her favorite game, Balloon Bouncer, over and over until she ran out of tokens. Balloon Bouncer costs
3
3
3
tokens per game, and Amy started with a bucket of
35
35
35
game tokens.
\newline
Which equation can Amy use to find how many games of Balloon Bouncer,
g
g
g
, she played?
\newline
Choices:
\newline
(A)
2
g
+
3
=
35
2g + 3 = 35
2
g
+
3
=
35
\newline
(B)
3
g
+
2
=
35
3g + 2 = 35
3
g
+
2
=
35
\newline
(C)
2
(
g
+
3
)
=
35
2(g + 3) = 35
2
(
g
+
3
)
=
35
\newline
(D)
3
(
g
+
2
)
=
35
3(g + 2) = 35
3
(
g
+
2
)
=
35
\newline
How many games of Balloon Bouncer did Amy play?
\newline
____ games
Get tutor help
Terrence signed up for the Safe Venture driving school. He will spend
10
10
10
hours driving with an instructor and will also attend weekly
2
2
2
-hour classes. When Terrence completes the
26
26
26
total hours of instruction, he will take his driver's test.
\newline
Which equation can you use to find
w
w
w
, the number of weeks the driving classes last?
\newline
Choices:
\newline
(A)
10
w
+
2
=
26
10w + 2 = 26
10
w
+
2
=
26
\newline
(B)
2
(
w
+
10
)
=
26
2(w + 10) = 26
2
(
w
+
10
)
=
26
\newline
(C)
2
w
+
10
=
26
2w + 10 = 26
2
w
+
10
=
26
\newline
(D)
10
(
w
+
2
)
=
26
10(w + 2) = 26
10
(
w
+
2
)
=
26
\newline
How many weeks do the driving classes last?
\newline
____ weeks
Get tutor help
At the start of her shift at Midtown Bakery, Megan made some batches of cookies that called for
3
3
3
cups of flour each. Then, she used the remaining
8
8
8
cups of flour she had to make a pan of muffins. She started her shift with a
20
20
20
-cup bag of flour.
\newline
Which equation can you use to find how many batches of cookies,
x
x
x
, Megan made?
\newline
Choices:
\newline
(A)
3
(
x
+
8
)
=
20
3(x + 8) = 20
3
(
x
+
8
)
=
20
\newline
(B)
8
x
+
3
=
20
8x + 3 = 20
8
x
+
3
=
20
\newline
(C)
8
(
x
+
3
)
=
20
8(x + 3) = 20
8
(
x
+
3
)
=
20
\newline
(D)
3
x
+
8
=
20
3x + 8 = 20
3
x
+
8
=
20
\newline
How many batches of cookies did Megan make?
\newline
Write your answer as a whole number or a simplified fraction.
\newline
____ batches of cookies
Get tutor help
Maplewood Furniture Store is having a sale on dining room furniture. When a customer purchases a set of dining chairs, a one-time discount of
55
55
55
$
\$
$
is applied to the total. During the sale, Rhianna buys a set of
6
6
6
chairs that match the table she inherited from her grandmother. Rhianna pays
455
455
455
$
\$
$
in all.
\newline
Which equation can you use to find the regular cost,
c
c
c
, of each chair?
\newline
Choices:
\newline
(A)
6
c
−
55
=
455
6c - 55 = 455
6
c
−
55
=
455
\newline
(B)
55
c
−
6
=
455
55c - 6 = 455
55
c
−
6
=
455
\newline
(C)
6
(
c
−
55
)
=
455
6(c - 55) = 455
6
(
c
−
55
)
=
455
\newline
(D)
55
(
c
−
6
)
=
455
55(c - 6) = 455
55
(
c
−
6
)
=
455
\newline
What is the regular cost of each chair?
\newline
____
$
\$
$
Get tutor help
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