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Math Problems
Algebra 1
Solve a system of equations using any method: word problems
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
\newline
A camp counselor for a summer day camp sometimes buys lunch for her campers at a nearby fast food restaurant. On Monday, she purchased
1
1
1
hamburger kid meal and
3
3
3
chicken nugget kid meals, for a total of
$
14
\$14
$14
. On Thursday, she spent
$
36
\$36
$36
on
4
4
4
hamburger kid meals and
7
7
7
chicken nugget kid meals. How much does each type of meal cost?
\newline
Each hamburger meal costs
$
\$
$
_____, and each chicken nugget meal costs
$
\$
$
_____.
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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
\newline
Janelle and Duncan are comparing the international calling plans on their cell phones. On her plan, Janelle pays
$
1
\$1
$1
just to place a call and
$
5
\$5
$5
for each minute. When Duncan makes an international call, he pays
$
5
\$5
$5
to place the call and
$
1
\$1
$1
for each minute. A call of a certain duration would cost exactly the same under both plans. What is the duration? What is the cost?
\newline
A call of
_
_
\_\_
__
minutes would cost
$
_
_
\$\_\_
$__
under each plan.
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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
\newline
A realtor is decorating some homes for sale, putting a certain number of decorative pillows on each twin bed and a certain number on each queen bed. In one house, she decorated
4
4
4
twin beds and
2
2
2
queen beds and used a total of
42
42
42
pillows. At another house, she used
31
31
31
pillows to spruce up
4
4
4
twin beds and
1
1
1
queen bed. How many decorative pillows did the realtor arrange on each bed?
\newline
The realtor used
_
_
_
\_\_\_
___
pillows on every twin bed and
_
_
_
\_\_\_
___
pillows on every queen bed.
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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
\newline
Nick and his cousin are playing a game where they pick up colored sticks. Nick currently has
14
14
14
points and likes to pick up the green sticks, earning
9
9
9
points every turn. His cousin just lost all her points on the previous turn, and has a strategy to catch up by getting all the pink ones, earning
10
10
10
points per turn. In a certain number of turns, the score will be tied. How long will that take? How many points will they each have?
\newline
In
_
\_
_
turns, both players will have
_
\_
_
points.
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Natasha and her two dogs were walking on a perfectly straight road when her two dogs ran away from her in opposite directions. Her beagle is now
25
4
\frac{25}{4}
4
25
meters directly to her right, and her labrador is
51
20
\frac{51}{20}
20
51
meters directly to her left.
\newline
Which
2
2
2
of the following expressions represents how far apart the two dogs are?
\newline
Choose
2
2
2
answers:
\newline
(A)
∣
25
4
+
51
20
∣
\left|\frac{25}{4}+\frac{51}{20}\right|
∣
∣
4
25
+
20
51
∣
∣
\newline
(B)
∣
−
51
20
+
25
4
∣
\left|-\frac{51}{20}+\frac{25}{4}\right|
∣
∣
−
20
51
+
4
25
∣
∣
\newline
(C)
∣
−
51
20
−
25
4
∣
\left|-\frac{51}{20}-\frac{25}{4}\right|
∣
∣
−
20
51
−
4
25
∣
∣
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Becky tried to evaluate an expression step by step.
\newline
4
5
+
7
−
5
4
=
4
5
−
5
4
+
7
Step
1
=
0
+
7
Step 2
=
7
Step
3
\begin{array}{l} \frac{4}{5}+7-\frac{5}{4} \\ =\frac{4}{5}-\frac{5}{4}+7 \quad \text { Step } 1 \\ =0+7 \quad \text { Step 2 } \\ =7 \quad \text { Step } 3 \\ \end{array}
5
4
+
7
−
4
5
=
5
4
−
4
5
+
7
Step
1
=
0
+
7
Step 2
=
7
Step
3
\newline
Find Becky's first mistake.
\newline
Choose
1
1
1
answer:
\newline
(A) Commuting a negative term changes the value.
\newline
(B)
4
5
\frac{4}{5}
5
4
minus
5
4
\frac{5}{4}
4
5
equals
−
9
20
-\frac{9}{20}
−
20
9
, not
0
0
0
\newline
(C)
0
0
0
plus
7
7
7
equals
0
0
0
, not
7
7
7
.
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Raul tried to evaluate an expression step by step.
\newline
3
−
(
−
5
)
−
7
=
3
+
5
−
7
Step
1
=
3
+
2
Step 2
=
5
Step
3
\begin{array}{l} 3-(-5)-7 \\ =3+5-7 \quad \text { Step } 1 \\ =3+2 \quad \text { Step 2 } \\ =5 \quad \text { Step } 3 \\ \end{array}
3
−
(
−
5
)
−
7
=
3
+
5
−
7
Step
1
=
3
+
2
Step 2
=
5
Step
3
\newline
Find Raul's first mistake.
\newline
Choose
1
1
1
answer:
\newline
(A) The opposite of
−
5
-5
−
5
is
−
5
-5
−
5
, not
5
5
5
.
\newline
(B)
5
5
5
minus
7
7
7
equals
−
2
-2
−
2
, not
2
2
2
.
\newline
(C)
3
3
3
plus
2
2
2
equals
6
6
6
, not
5
5
5
.
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Amber tried to evaluate an expression step by step.
\newline
−
3
−
(
−
5
)
+
4
=
−
3
+
5
+
4
Step
1
=
−
3
+
9
Step 2
=
−
12
Step
3
\begin{array}{l} -3-(-5)+4 \\ =-3+5+4 \quad \text { Step } 1 \\ =-3+9 \quad \text { Step 2 } \\ =-12 \quad \text { Step } 3 \\ \end{array}
−
3
−
(
−
5
)
+
4
=
−
3
+
5
+
4
Step
1
=
−
3
+
9
Step 2
=
−
12
Step
3
\newline
Find Amber's first mistake.
\newline
Choose
1
1
1
answer:
\newline
(A) The opposite of
−
5
-5
−
5
is
−
5
-5
−
5
, not
5
5
5
.
\newline
(B) Adding from right to left changes the sum's value.
\newline
(C)
−
3
-3
−
3
plus
9
9
9
equals
6
6
6
, not
−
12
-12
−
12
.
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New policies reduced the overuse of water in an area. The water table in that area went up by
1
1
1
.
2
2
2
meters in one year. The water table was
12
12
12
.
5
5
5
meters below the surface at the start of the year.
\newline
The following equation describes this situation.
\newline
−
12.5
+
1.2
=
−
11.3
-12.5+1.2=-11.3
−
12.5
+
1.2
=
−
11.3
\newline
What does
−
11
-11
−
11
.
3
3
3
tell us?
\newline
Choose
1
1
1
answer:
\newline
(A) The water table was
11
11
11
.
3
3
3
meters below the surface at the end of the year.
\newline
(B) The water table went down by
11
11
11
.
3
3
3
meters in one year.
\newline
(C) Each household used
11
11
11
.
3
3
3
fewer liters of water during the year.
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Josiah is cooking a piece of lamb. Before he puts it in the oven, the internal temperature of the lamb is
4
1
∘
C
41^{\circ} \mathrm{C}
4
1
∘
C
below the final temperature it needs to reach. The outside of the lamb heats up faster than the inside. Josiah takes the lamb out of the oven when the internal temperature is still
6
∘
C
6^{\circ} \mathrm{C}
6
∘
C
below the final temperature it needs to reach, so the inside and outside can balance out to the right final temperature.
\newline
Josiah wonders how much the internal temperature had changed when he removed the lamb from the oven.
\newline
Which of the following equations matches the situation above?
\newline
Choose
1
1
1
answer:
\newline
(A)
41
+
6
=
41+6=
41
+
6
=
?
\newline
(B)
−
41
+
?
=
−
6
-41+?=-6
−
41
+
?
=
−
6
\newline
(C)
41
+
?
=
6
41+?=6
41
+
?
=
6
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Eric was rock climbing. At one point, he stopped and climbed straight down
2
1
2
2 \frac{1}{2}
2
2
1
meters. Then he climbed straight up
6
3
4
6 \frac{3}{4}
6
4
3
meters. Eric was wondering what his change in elevation was after these two moves.
\newline
Which of the following equations matches the situation above?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
2
1
2
−
6
3
4
=
-2 \frac{1}{2}-6 \frac{3}{4}=
−
2
2
1
−
6
4
3
=
?
\newline
(B)
2
1
2
−
6
3
4
=
2 \frac{1}{2}-6 \frac{3}{4}=
2
2
1
−
6
4
3
=
?
\newline
(C)
−
2
1
2
+
6
3
4
=
-2 \frac{1}{2}+6 \frac{3}{4}=
−
2
2
1
+
6
4
3
=
?
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Amy hikes down a slope to a lake that is
10
10
10
.
2
2
2
meters below the trail. Then Amy jumps into the lake, and swims
1
1
1
.
5
5
5
meters down. She wonders what her new height is relative to the trail.
\newline
Which of the following equations matches the situation above?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
10.2
+
1.5
=
-10.2+1.5=
−
10.2
+
1.5
=
?
\newline
(B)
10.2
−
1.5
=
10.2-1.5=
10.2
−
1.5
=
?
\newline
(C)
−
10.2
−
1.5
=
-10.2-1.5=
−
10.2
−
1.5
=
?
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Last night, the minimum temperature was
−
2
3
∘
C
-23^{\circ} \mathrm{C}
−
2
3
∘
C
. That was
5
∘
C
5^{\circ} \mathrm{C}
5
∘
C
warmer than the lowest temperature where Ailen can safely use her sleeping bag.
\newline
The following equation describes this situation.
\newline
−
28
+
5
=
−
23
-28+5=-23
−
28
+
5
=
−
23
\newline
What does
−
28
-28
−
28
tell us?
\newline
Choose
1
1
1
answer:
\newline
(A) The temperature dropped
2
8
∘
C
28^{\circ} \mathrm{C}
2
8
∘
C
overnight.
\newline
(B) The temperature was
2
8
∘
C
28^{\circ} \mathrm{C}
2
8
∘
C
too cold for using the sleeping bag.
\newline
(C) Ailen can safely use her sleeping bag down to
−
2
8
∘
C
-28^{\circ} \mathrm{C}
−
2
8
∘
C
.
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Vitor is going to guess on all
40
40
40
questions of his multiple-choice test. Each question on the test has
5
5
5
answer options.
\newline
Complete the following statement with the best prediction.
\newline
Vitor will correctly answer...
\newline
Choose
1
1
1
answer:
\newline
(A) Exactly
8
8
8
questions
\newline
(B) Close to
8
8
8
questions but probably not exactly
8
8
8
questions
\newline
(C) Exactly
20
20
20
questions
\newline
(D) Close to
20
20
20
questions but probably not exactly
20
20
20
questions
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Eiko is wearing a magic ring that increases the power of her healing spell by
30
%
30 \%
30%
. Without the ring, her healing spell restores
H
H
H
health points.
\newline
Which of the following expressions could represent how many health points the spell restores when Eiko is wearing the magic ring?
\newline
Choose
2
2
2
answers:
\newline
0.7
H
0.7 H
0.7
H
\newline
130
100
H
\frac{130}{100} H
100
130
H
\newline
(
3
10
+
1
)
H
\left(\frac{3}{10}+1\right) H
(
10
3
+
1
)
H
\newline
H
−
0.30
H
H-0.30 H
H
−
0.30
H
\newline
30
+
H
30+H
30
+
H
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Jose tracks how many times he got fast food each month. He got fast food
12
12
12
times in January,
10
10
10
times in February,
18
18
18
times in March,
4
4
4
times in April, and
2
2
2
times in May.
\newline
Find the mean number of times Jose got fast food.
\newline
times getting fast food
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Scarlett Squirrel teaches a hula dancing class to young squirrels.
14
14
14
squirrels showed up to class on Monday,
10
10
10
squirrels on Tuesday,
8
8
8
squirrels on Wednesday,
10
10
10
squirrels on Thursday, and
12
12
12
squirrels on Friday.
\newline
Find the mean number of squirrels. squirrels
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Justin did push-ups every weekday this week. He did
8
8
8
push-ups on Monday,
14
14
14
push-ups on Tuesday,
18
18
18
push-ups on Wednesday,
6
6
6
push-ups on Thursday, and
8
8
8
pushups on Friday.
\newline
Find the mean number of push-ups.
\newline
push-ups
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Seth is planning a route for a train that travels at a constant rate of
220
220
220
kilometers per hour. They want to write an equation that shows how many hours
(
t
)
(t)
(
t
)
a trip takes in terms of the trip's distance
(
d
)
(d)
(
d
)
.
\newline
How should Seth write their equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
t
=
d
220
t=\frac{d}{220}
t
=
220
d
\newline
(B)
d
t
=
220
\frac{d}{t}=220
t
d
=
220
\newline
(C)
d
=
220
t
d=220 t
d
=
220
t
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3
3
3
folders cost
$
2.91
\$ 2.91
$2.91
.
\newline
Which equation would help determine the cost of
2
2
2
folders?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
$
2.91
=
x
3
\frac{2}{\$ 2.91}=\frac{x}{3}
$2.91
2
=
3
x
\newline
(B)
2
x
=
3
$
2.91
\frac{2}{x}=\frac{3}{\$ 2.91}
x
2
=
$2.91
3
\newline
(C)
x
2
=
3
$
2.91
\frac{x}{2}=\frac{3}{\$ 2.91}
2
x
=
$2.91
3
\newline
(D)
2
x
=
$
2.91
3
\frac{2}{x}=\frac{\$ 2.91}{3}
x
2
=
3
$2.91
\newline
(E) None of the above
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5
5
5
markers cost
$
6.55
\$ 6.55
$6.55
.
\newline
Which equation would help determine the cost of
4
4
4
markers?
\newline
Choose
1
1
1
answer:
\newline
(A)
4
5
=
$
6.55
x
\frac{4}{5}=\frac{\$ 6.55}{x}
5
4
=
x
$6.55
\newline
(B)
4
$
6.55
=
x
5
\frac{4}{\$ 6.55}=\frac{x}{5}
$6.55
4
=
5
x
\newline
(C)
5
4
=
x
$
6.55
\frac{5}{4}=\frac{x}{\$ 6.55}
4
5
=
$6.55
x
\newline
(D)
4
x
=
$
6.55
5
\frac{4}{x}=\frac{\$ 6.55}{5}
x
4
=
5
$6.55
\newline
(E) None of the above
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Sharon tried to solve an equation step by step.
\newline
9
=
−
3
(
e
−
2
)
9
=
−
3
e
+
6
Step
1
15
=
3
e
Step 2
\begin{array}{l} 9=-3(e-2) \\ 9=-3 e+6 \quad \text { Step } 1 \\ 15=3 e \quad \text { Step 2 } \\ \end{array}
9
=
−
3
(
e
−
2
)
9
=
−
3
e
+
6
Step
1
15
=
3
e
Step 2
\newline
5
=
e
Step 3
5=e \quad \text { Step 3 }
5
=
e
Step 3
\newline
Find Sharon's mistake.
\newline
Choose
1
1
1
answer:
\newline
(A) Step
1
1
1
\newline
(B) Step
2
2
2
\newline
(C)
Step
3
\operatorname{Step} 3
Step
3
\newline
(D) Sharon did not make a mistake.
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7
7
7
watermelons cost
$
8.96
\$ 8.96
$8.96
.
\newline
Which equation would help determine the cost of
5
5
5
watermelons?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
5
=
$
8.96
7
\frac{x}{5}=\frac{\$ 8.96}{7}
5
x
=
7
$8.96
\newline
(B)
x
5
=
7
$
8.96
\frac{x}{5}=\frac{7}{\$ 8.96}
5
x
=
$8.96
7
\newline
(C)
7
5
=
x
$
8.96
\frac{7}{5}=\frac{x}{\$ 8.96}
5
7
=
$8.96
x
\newline
(D)
5
x
=
$
8.96
7
\frac{5}{x}=\frac{\$ 8.96}{7}
x
5
=
7
$8.96
\newline
(E) None of the above
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9
9
9
pencils cost
$
7.74
\$ 7.74
$7.74
.
\newline
Which equation would help determine the cost of
6
6
6
pencils?
\newline
Choose
1
1
1
answer:
\newline
(A)
6
x
=
9
$
7.74
\frac{6}{x}=\frac{9}{\$ 7.74}
x
6
=
$7.74
9
\newline
(B)
x
6
=
9
$
7.74
\frac{x}{6}=\frac{9}{\$ 7.74}
6
x
=
$7.74
9
\newline
(C)
9
6
=
x
$
7.74
\frac{9}{6}=\frac{x}{\$ 7.74}
6
9
=
$7.74
x
\newline
(D)
6
x
=
$
7.74
9
\frac{6}{x}=\frac{\$ 7.74}{9}
x
6
=
9
$7.74
\newline
(E) None of the above
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3
3
3
erasers cost
$
4.41
\$ 4.41
$4.41
.
\newline
Which equation would help determine the cost of
4
4
4
erasers?
\newline
Choose
1
1
1
answer:
\newline
(A)
4
x
=
$
4.41
3
\frac{4}{x}=\frac{\$ 4.41}{3}
x
4
=
3
$4.41
\newline
(B)
4
$
4.41
=
x
3
\frac{4}{\$ 4.41}=\frac{x}{3}
$4.41
4
=
3
x
\newline
(C)
4
3
=
$
4.41
x
\frac{4}{3}=\frac{\$ 4.41}{x}
3
4
=
x
$4.41
\newline
(D)
4
x
=
3
$
4.41
\frac{4}{x}=\frac{3}{\$ 4.41}
x
4
=
$4.41
3
\newline
(E) None of the above
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3
3
3
markers cost
$
5.79
\$ 5.79
$5.79
.
\newline
Which equation would help determine the cost of
13
13
13
markers?
\newline
Choose
1
1
1
answer:
\newline
(A)
13
$
5.79
=
x
3
\frac{13}{\$ 5.79}=\frac{x}{3}
$5.79
13
=
3
x
\newline
(B)
x
13
=
3
$
5.79
\frac{x}{13}=\frac{3}{\$ 5.79}
13
x
=
$5.79
3
\newline
(C)
3
$
5.79
=
13
x
\frac{3}{\$ 5.79}=\frac{13}{x}
$5.79
3
=
x
13
\newline
(D)
13
x
=
$
5.79
3
\frac{13}{x}=\frac{\$ 5.79}{3}
x
13
=
3
$5.79
\newline
(E) None of the above
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Jessie tried to solve an equation step by step.
\newline
1.5
b
+
9
=
11
1.5 b+9=11
1.5
b
+
9
=
11
\newline
1.5
b
=
3
Step
1
1.5 b=3 \quad \text { Step } 1
1.5
b
=
3
Step
1
\newline
b
=
2
Step
2
b=2 \quad \text { Step } 2
b
=
2
Step
2
\newline
Find Jessie's mistake.
\newline
Choose
1
1
1
answer:
\newline
(A) Step
1
1
1
\newline
(B) Step
2
2
2
\newline
(C) Jessie did not make a mistake.
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Leon tried to solve an equation step by step.
\newline
1
2
w
−
12
=
18
1
2
w
=
30
Step
1
w
=
15
Step 2
\begin{aligned} \frac{1}{2} w-12 & =18 \\ \frac{1}{2} w & =30 \quad \text { Step } 1 \\ w & =15 \quad \text { Step 2 } \end{aligned}
2
1
w
−
12
2
1
w
w
=
18
=
30
Step
1
=
15
Step 2
\newline
Find Leon's mistake.
\newline
Choose
1
1
1
answer:
\newline
(A)
Step
1
\operatorname{Step} 1
Step
1
\newline
(B) Step
2
2
2
\newline
(C) Leon did not make a mistake.
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Olga tried to solve an equation step by step.
\newline
1
4
(
1
3
k
+
9
)
=
6
1
3
k
+
9
=
24
Step 1
1
3
k
=
15
Step 2
k
=
5
Step 3
\begin{array}{rlrl} \frac{1}{4}\left(\frac{1}{3} k+9\right) & =6 & \\ \frac{1}{3} k+9 & =24 \quad \text { Step 1 } \\ \frac{1}{3} k & =15 \quad \text { Step 2 } \\ k & =5 \quad \text { Step 3 } \end{array}
4
1
(
3
1
k
+
9
)
3
1
k
+
9
3
1
k
k
=
6
=
24
Step 1
=
15
Step 2
=
5
Step 3
\newline
Find Olga's mistake.
\newline
Choose
1
1
1
answer:
\newline
(A) Step
1
1
1
\newline
(B) Step
2
2
2
\newline
(C)
Step
3
\operatorname{Step} 3
Step
3
\newline
D Olga did not make a mistake.
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Jeremy and Robin like to collect nickels. Jeremy has
n
n
n
nickels, and Robin has
55
55
55
nickels. Together they have a total of
100
100
100
nickels.
\newline
Write an equation to describe this situation.
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Melissa and Rachel like to make funny hats. Melissa has made
20
20
20
zebra-printed hats, and Rachel has made
h
h
h
striped hats. Together they have made a total of
42
42
42
hats.
\newline
Write an equation to describe this situation.
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Marcos is bringing
36
36
36
cookies to his book club, but he's not sure how many people will be there. He wants to write an equation that shows how many cookies each person will get
(
c
)
(c)
(
c
)
in terms of how many people are there
(
n
)
(n)
(
n
)
.
\newline
How should Marcos write his equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
c
=
36
n
c=\frac{36}{n}
c
=
n
36
\newline
(B)
n
=
36
c
n=\frac{36}{c}
n
=
c
36
\newline
(C)
n
c
=
36
n c=36
n
c
=
36
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Caleb is solving the following equation for
x
x
x
.
\newline
x
=
x
+
2
+
7
x=\sqrt{x+2}+7
x
=
x
+
2
+
7
\newline
His first few steps are given below.
\newline
x
−
7
=
x
+
2
(
x
−
7
)
2
=
(
x
+
2
)
2
x
2
−
14
x
+
49
=
x
+
2
\begin{aligned} x-7 & =\sqrt{x+2} \\ (x-7)^{2} & =(\sqrt{x+2})^{2} \\ x^{2}-14 x+49 & =x+2 \end{aligned}
x
−
7
(
x
−
7
)
2
x
2
−
14
x
+
49
=
x
+
2
=
(
x
+
2
)
2
=
x
+
2
\newline
Is it necessary for Caleb to check his answers for extraneous solutions?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
Dimitri is solving the following equation for
x
x
x
.
\newline
2
x
2
−
7
=
33
2 x^{2}-7=33
2
x
2
−
7
=
33
\newline
His first few steps are given below.
\newline
2
x
2
=
40
2 x^{2}=40
2
x
2
=
40
\newline
x
2
=
20
x^{2}=20
x
2
=
20
\newline
x
=
±
20
x= \pm \sqrt{20}
x
=
±
20
\newline
Is it necessary for Dimitri to check his answers for extraneous solutions?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
Emily is solving the following equation for
z
z
z
.
\newline
z
−
8
=
3
z
−
5
z-8=\sqrt{3 z-5}
z
−
8
=
3
z
−
5
\newline
Her first few steps are given below.
\newline
(
z
−
8
)
2
=
(
3
z
−
5
)
2
z
2
−
16
z
+
64
=
3
z
−
5
\begin{aligned} (z-8)^{2} & =(\sqrt{3 z-5})^{2} \\ z^{2}-16 z+64 & =3 z-5 \end{aligned}
(
z
−
8
)
2
z
2
−
16
z
+
64
=
(
3
z
−
5
)
2
=
3
z
−
5
\newline
Is it necessary for Emily to check her answers for extraneous solutions?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
Ahmed is solving the following equation for
x
x
x
.
\newline
2
x
−
7
3
+
11
=
3
2 \sqrt[3]{x-7}+11=3
2
3
x
−
7
+
11
=
3
\newline
His first few steps are given below.
\newline
2
x
−
7
3
=
−
8
x
−
7
3
=
−
4
(
x
−
7
3
)
3
=
(
−
4
)
3
x
−
7
=
−
64
\begin{aligned} 2 \sqrt[3]{x-7} & =-8 \\ \sqrt[3]{x-7} & =-4 \\ (\sqrt[3]{x-7})^{3} & =(-4)^{3} \\ x-7 & =-64 \end{aligned}
2
3
x
−
7
3
x
−
7
(
3
x
−
7
)
3
x
−
7
=
−
8
=
−
4
=
(
−
4
)
3
=
−
64
\newline
Is it necessary for Ahmed to check his answers for extraneous solutions?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
Get tutor help
A chameleon is looking for prey. Let positive numbers represent the elevation of prey above the chameleon and negative numbers represent the elevation of prey below the chameleon.
\newline
The chameleon spots a fly at
4
m
4 \mathrm{~m}
4
m
and a grasshopper at
−
6
m
-6 \mathrm{~m}
−
6
m
.
\newline
What does an elevation of
0
m
0 \mathrm{~m}
0
m
represent in this situation?
\newline
Choose
1
1
1
answer:
\newline
(A) The elevation of the fly
\newline
(B) The elevation of the chameleon
\newline
(C) The elevation of the grasshopper
Get tutor help
An arithmetic sequence is defined as follows:
\newline
{
a
1
=
−
138
a
i
=
a
i
−
1
+
6
\left\{\begin{array}{l} a_{1}=-138 \\ a_{i}=a_{i-1}+6 \end{array}\right.
{
a
1
=
−
138
a
i
=
a
i
−
1
+
6
\newline
Find the sum of the first
35
35
35
terms in the sequence.
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José is on a gameshow that involves a taste test. He gets to see a list of
15
15
15
different secret ingredients before tasting
3
3
3
dishes one after the other. The
3
3
3
dishes are all identical to each other except that each dish contains
1
1
1
of the
15
15
15
secret ingredients. He gets
60
60
60
seconds to identify what secret ingredient was in each dish.
\newline
The permutation formula
n
P
r
n \mathrm{P} r
n
P
r
can be used to find the number of unique ways to arrange the ingredients in the dishes.
\newline
What are the appropriate values of
n
n
n
and
r
r
r
?
\newline
n
=
□
r
=
□
\begin{array}{l} n=\square \\ r=\square \end{array}
n
=
□
r
=
□
Get tutor help
A small college with
1
1
1
,
200
200
200
total students has a student government of
40
40
40
members. From its members, the student government will elect a president, vice president, secretary, and treasurer. No single member can hold more than
1
1
1
of these
4
4
4
positions.
\newline
The permutation formula
n
P
r
n \mathrm{Pr}
n
Pr
can be used to find the number of unique ways the student government can arrange its members into these positions.
\newline
What are the appropriate values of
n
n
n
and
r
r
r
?
\newline
n
=
□
r
=
□
\begin{array}{l} n=\square \\ r=\square \end{array}
n
=
□
r
=
□
Get tutor help
Priya's favorite singer has made
6
6
6
albums containing
75
75
75
songs in total. Priya wants to make a playlist of
10
10
10
of those songs, and she won't repeat
1
1
1
of the
75
75
75
songs.
\newline
The permutation formula
n
P
r
n \mathrm{Pr}
n
Pr
can be used to find the number of unique ways Priya can pick and arrange the songs for the playlist.
\newline
What are the appropriate values of
n
n
n
and
r
r
r
?
\newline
n
=
r
=
\begin{array}{l} n= \\ r= \end{array}
n
=
r
=
Get tutor help
A biology teacher has
5
5
5
different pets they keep in their classroom. For an upcoming holiday break, the teacher will send the pets home with students. Suppose that
16
16
16
of the teacher's
75
75
75
students volunteer to take a pet home, and the teacher will randomly select
5
5
5
of those volunteers to each take
1
1
1
pet home.
\newline
The permutation formula
n
P
r
n \mathrm{P} r
n
P
r
can be used to find the number of unique ways the teacher can distribute pets to the volunteers.
\newline
What are the appropriate values of
n
n
n
and
r
r
r
?
\newline
n
=
□
r
=
□
\begin{array}{l} n=\square \\ r=\square \end{array}
n
=
□
r
=
□
Get tutor help
Gottfried wanted to see how contagious yawning can be. To better understand this, he conducted a social experiment by yawning in front of a random large crowd and observing how many people yawned as a result.
\newline
The relationship between the elapsed time
t
t
t
, in minutes, since Gottfried yawned, and the number of people in the crowd,
P
minute
(
t
)
P_{\text {minute }}(t)
P
minute
(
t
)
, who yawned as a result is modeled by the following function:
\newline
P
minute
(
t
)
=
5
⋅
(
1.03
)
t
P_{\text {minute }}(t)=5 \cdot(1.03)^{t}
P
minute
(
t
)
=
5
⋅
(
1.03
)
t
\newline
Complete the following sentence about the hourly rate of change in the number of people who yawn in Gottfried's experiment.
\newline
Round your answer to two decimal places.
\newline
Every hour, the number of people who yawn in Gottfried's experiment grows by a factor of
Get tutor help
The population of Springville is on the rise. Each year, on January
1
1
1
, the town holds its own census and the population is recorded. In
2010
2010
2010
, the town recorded a population of
12
12
12
,
000
000
000
. The
2011
2011
2011
census reported a
5
%
5 \%
5%
increase from the
2010
2010
2010
population, and the
2012
2012
2012
census reported a
7
%
7 \%
7%
increase from the
2011
2011
2011
population. By how many people did the population of Springville increase over the
2
2
2
-year period?
\newline
Choose
1
1
1
answer:
\newline
(A)
240
240
240
\newline
(B)
882
882
882
\newline
(C)
1440
\mathbf{1 4 4 0}
1440
\newline
(D)
1482
\mathbf{1 4 8 2}
1482
Get tutor help
In School District X,
6.9
%
6.9 \%
6.9%
of the
29
29
29
students in Ms. Walker's sixthgrade class identify as Asian. The average sixth-grade class size in the school district is
29
29
29
. If the students in Ms. Walker's class are representative of students in the school district's sixth-grade classes and there are
112
112
112
sixth-grade classes in the district, which of the following best estimates the number of sixth-grade students in the school district who do not identify as Asian?
\newline
Choose
1
1
1
answer:
\newline
(A)
3
3
3
,
248
248
248
\newline
(B)
3
3
3
,
024
024
024
\newline
(C)
1
1
1
,
007
007
007
\newline
(D)
224
224
224
Get tutor help
In a random sample of
200
200
200
U.S. adults,
152
152
152
have read at least one book in the past
12
12
12
months. Based on this information, approximately how many of the
255
255
255
million U.S. adults have not read a book in the past
12
12
12
months?
\newline
Choose
1
1
1
answer:
\newline
(A)
48
48
48
million
\newline
(B)
61
61
61
million
\newline
(C)
103
\mathbf{1 0 3}
103
million
\newline
(D)
194
\mathbf{1 9 4}
194
million
Get tutor help
Takada is hosting an event for
100
100
100
of her fans. For the event, she meets each of her fans one at a time at a constant rate. After
90
90
90
minutes, she has met
45
%
45 \%
45%
of her fans at the event. Which of the following equations models the number of fans,
F
F
F
, remaining for Takada to meet
m
m
m
minutes after the event started?
\newline
Choose
1
1
1
answer:
\newline
(A)
F
=
100
−
0.5
m
F=100-0.5 m
F
=
100
−
0.5
m
\newline
(B)
F
=
100
−
0.45
m
F=100-0.45 m
F
=
100
−
0.45
m
\newline
(C)
F
=
100
(
0.45
)
m
90
F=100(0.45)^{\frac{m}{90}}
F
=
100
(
0.45
)
90
m
\newline
(D)
F
=
100
(
0.55
)
m
90
F=100(0.55)^{\frac{m}{90}}
F
=
100
(
0.55
)
90
m
Get tutor help
The nutrition facts on a container of mini pretzels state that each serving of the mini pretzels contains
310
310
310
milligrams of sodium, which is
13
%
13 \%
13%
of the recommended daily value for adults. If
x
x
x
servings of mini pretzels contain
p
p
p
percent of an adult's recommended daily value of sodium, which of the following expresses
p
p
p
in terms of
x
x
x
?
\newline
Choose
1
1
1
answer:
\newline
(A)
p
=
(
1.13
)
x
p=(1.13)^{x}
p
=
(
1.13
)
x
\newline
(B)
p
=
310
(
0.13
)
x
p=310(0.13)^{x}
p
=
310
(
0.13
)
x
\newline
(C)
p
=
13
x
p=13 x
p
=
13
x
\newline
(D)
p
=
310
(
0.13
x
)
p=310(0.13 x)
p
=
310
(
0.13
x
)
Get tutor help
A new shopping mall records
150
150
150
total shoppers on their first day of business. Each day after that, the number of shoppers is
15
%
15 \%
15%
more than the number of shoppers the day before.
\newline
Which expression gives the total number of shoppers in the first
n
n
n
days of business?
\newline
Choose
1
1
1
answer:
\newline
(A)
1.15
(
1
−
15
0
n
1
−
150
)
1.15\left(\frac{1-150^{n}}{1-150}\right)
1.15
(
1
−
150
1
−
15
0
n
)
\newline
(B)
0.85
(
1
−
15
0
n
1
−
150
)
0.85\left(\frac{1-150^{n}}{1-150}\right)
0.85
(
1
−
150
1
−
15
0
n
)
\newline
(C)
150
(
1
−
1.1
5
n
1
−
1.15
)
150\left(\frac{1-1.15^{n}}{1-1.15}\right)
150
(
1
−
1.15
1
−
1.1
5
n
)
\newline
(D)
150
(
1
−
0.8
5
n
1
−
0.85
)
150\left(\frac{1-0.85^{n}}{1-0.85}\right)
150
(
1
−
0.85
1
−
0.8
5
n
)
Get tutor help
A high school's graduation rate is defined to be the percentage of the senior class that graduates. Last year
406
406
406
of Sagamore High School's
452
452
452
seniors graduated. This year the school expects the previous year's graduation rate to increase by approximately
2
2
2
percentage points. If there are
436
436
436
students in this year's senior class, which of the following best approximates the number of seniors that Sagamore High School expects to graduate this year?
\newline
Choose
1
1
1
answer:
\newline
(A)
390
390
390
students
\newline
(B)
400
400
400
students
\newline
(C)
410
410
410
students
\newline
(D)
420
420
420
students
Get tutor help
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