Resources
Testimonials
Plans
Sign in
Sign up
Resources
Testimonials
Plans
Home
Math Problems
Grade 6
Find a value using two-variable equations
A single processor takes
20
20
20
milliseconds
(
ms
)
(\text{ms})
(
ms
)
to prepare data entries and
0.1
n
0.1n
0.1
n
ms to copy the entries, where
n
n
n
is the number of entries. A multiprocessor takes
70
70
70
ms to prepare and copy one data entry, and whenever the number of entries is doubled the amount of time to prepare and copy them increases by
5
5
5
ms. Given
120
120
120
ms to prepare and copy data entries, which processor type can prepare and copy more entries and how many more entries can it prepare and copy?
\newline
Choose
1
1
1
answer:
\newline
(Choice A) The single processor can prepare and copy
176
176
176
more entries.
\newline
A The single processor can prepare and copy
176
176
176
more entries.
\newline
(Choice B) The single processor can prepare and copy
989
989
989
more entries.
\newline
B The single processor can prepare and copy
989
989
989
more entries.
\newline
(Choice C) The multiprocessor can prepare and copy
24
24
24
more entries.
\newline
C The multiprocessor can prepare and copy
24
24
24
more entries.
\newline
(Choice D) The multiprocessor can prepare and copy
1
,
012
1,012
1
,
012
more entries.
\newline
D The multiprocessor can prepare and copy
1
,
012
1,012
1
,
012
more entries.
Get tutor help
A single processor takes
20
20
20
milliseconds
(
ms
)
(\text{ms})
(
ms
)
to prepare data entries and
0.1
n
0.1n
0.1
n
ms to copy the entries, where
n
n
n
is the number of entries. A multiprocessor takes
70
70
70
ms to prepare and copy one data entry, and whenever the number of entries is doubled the amount of time to prepare and copy them increases by
5
5
5
ms. Given
120
120
120
ms to prepare and copy data entries, which processor type can prepare and copy more entries and how many more entries can it prepare and copy?
\newline
Choose
1
1
1
answer:
\newline
(Choice A) The single processor can prepare and copy
176
176
176
more entries.
\newline
A The single processor can prepare and copy
176
176
176
more entries.
\newline
(Choice B) The single processor can prepare and copy
989
989
989
more entries.
\newline
B The single processor can prepare and copy
989
989
989
more entries.
\newline
(Choice C) The multiprocessor can prepare and copy
24
24
24
more entries.
\newline
C The multiprocessor can prepare and copy
24
24
24
more entries.
\newline
(Choice D) The multiprocessor can prepare and copy
1
,
012
1,012
1
,
012
more entries.
\newline
D The multiprocessor can prepare and copy
1
,
012
1,012
1
,
012
more entries.
Get tutor help
The following table shows the number of fire hydrants in each neighborhood overseen by Fire District
9
9
9
Get tutor help
A single processor takes
20
20
20
milliseconds
(
ms
)
(\text{ms})
(
ms
)
to prepare data entries and
0.1
n
0.1n
0.1
n
ms to copy the entries, where
n
n
n
is the number of entries. A multiprocessor takes
70
70
70
ms to prepare and copy one data entry, and whenever the number of entries is doubled the amount of time to prepare and copy them increases by
5
5
5
ms. Given
120
120
120
ms to prepare and copy data entries, which processor type can prepare and copy more entries and how many more entries can it prepare and copy? Choose
1
1
1
answer:
\newline
(A) The single processor can prepare and copy
176
176
176
more entries.
\newline
(B) The single processor can prepare and copy
989
989
989
more entries.
\newline
(C) The multiprocessor can prepare and copy
(
ms
)
(\text{ms})
(
ms
)
0
0
0
more entries.
\newline
(D) The multiprocessor can prepare and copy
(
ms
)
(\text{ms})
(
ms
)
1
1
1
more entries.
Get tutor help
This equation shows how the amount of tape Gordon has used is related to the number of presents he has wrapped.
\newline
t
=
3
p
t = 3p
t
=
3
p
\newline
The variable
p
p
p
represents the number of presents wrapped, and the variable
t
t
t
represents the amount of tape used in centimeters. How much tape will Gordon need in all if he has to wrap
6
6
6
presents?
\newline
_____ centimeters
Get tutor help
This equation shows how Jamal's video game score is related to the number of coins he collects.
\newline
p
=
20
c
p = 20c
p
=
20
c
\newline
The variable
c
c
c
represents the number of coins he collects, and the variable
p
p
p
represents the total points he scores. After collecting a total of
1
1
1
coin, how many points will Jamal have scored in all?
\newline
_____ points
Get tutor help
This equation shows how the total pages of notes in Cassie's notebook depends on the number of hours she spends in class.
\newline
p
=
h
+
17
p = h + 17
p
=
h
+
17
\newline
The variable
h
h
h
represents the hours she spends in class, and the variable
p
p
p
represents the total pages of notes taken. After attending
3
3
3
hours of class, how many total pages of notes will Cassie have in her notebook?
\newline
_____ pages
Get tutor help
This equation shows how the total cost of visiting the science museum as a member is related to the number of visits.
\newline
c
=
v
+
16
c = v + 16
c
=
v
+
16
\newline
The variable
v
v
v
represents the number of visits to the science museum, and the variable
c
c
c
represents the total cost of those visits. For a member of the science museum, what is the total cost of
1
1
1
visit?
\newline
$
\$
$
_____
Get tutor help
This equation shows how the total amount of paper Martha's office has recycled depends on the number of weeks since they started the new recycling plan.
\newline
p
=
4
w
p = 4w
p
=
4
w
\newline
The variable
w
w
w
represents the number of weeks the office has been on the new recycling plan, and the variable
p
p
p
represents the total kilograms of paper recycled. After
5
5
5
weeks, how many kilograms of paper will Martha's office have recycled?
\newline
_____ kilograms
Get tutor help
This equation shows how the cost of Haley's birthday party depends on the number of guests.
\newline
c
=
g
+
8
c = g + 8
c
=
g
+
8
\newline
The variable
g
g
g
represents the number of guests, and the variable
c
c
c
represents the cost in dollars. If there are
8
8
8
guests, how much will Haley's birthday party cost?
\newline
$
\$
$
_
_
_
_
\_\_\_\_
____
Get tutor help
This equation shows how the time required to ring up a customer is related to the number of items being purchased.
\newline
t
=
p
+
18
t = p + 18
t
=
p
+
18
\newline
The variable
p
p
p
represents the number of items being purchased, and the variable
t
t
t
represents the time required to ring up the customer. How long does it take to ring up a customer with
2
2
2
items?
\newline
_____ seconds
Get tutor help
This equation shows how the total number of souvenirs Deion buys is related to the number of days he spends on vacation.
\newline
s
=
d
+
1
s = d + 1
s
=
d
+
1
\newline
The variable
d
d
d
represents the number of days he spends on vacation, and the variable
s
s
s
represents the total number of souvenirs he buys. After
3
3
3
days of vacation, how many total souvenirs will Deion have bought?
\newline
_____ souvenirs
Get tutor help
This equation shows how the total cost of visiting the science museum as a member is related to the number of visits.
\newline
c
=
10
v
c = 10v
c
=
10
v
\newline
The variable
v
v
v
represents the number of visits to the science museum, and the variable
c
c
c
represents the total cost of those visits. For a member of the science museum, what is the total cost of
1
1
1
visit?
\newline
$
\$
$
_____
Get tutor help
This equation shows how the total number of books Jack has read depends on the number of months he has been part of a book club.
\newline
b
=
m
+
12
b = m + 12
b
=
m
+
12
\newline
The variable
m
m
m
represents the number of months he has been a member of the book club, and the variable
b
b
b
represents the number of books that he has read. After belonging to the book club for
4
4
4
months, how many books will Jack have read in all?
\newline
_____ books
Get tutor help
Pick the story that can be modeled by the equation
5
x
=
75
5x = 75
5
x
=
75
.
\newline
Choices:
\newline
(A)Mabel tracks her reading for homework. Last night, she started a new book with
75
75
75
pages. So far, she's read
5
5
5
pages and has
x
x
x
pages left.
\newline
(B)Mabel tracks her reading for homework. Every night for
5
5
5
nights straight, she read for
x
x
x
minutes before bed. Mabel read for
75
75
75
minutes in all.
Get tutor help
Ms. Maynard brought
q
q
q
math quizzes home to grade over the weekend. She could only grade
31
31
31
of the quizzes on Saturday. So, she had
56
56
56
quizzes left to grade on Sunday.
\newline
Which diagram models the story?
\newline
Which equation models the story?
\newline
Choices:
\newline
(A)
q
−
31
=
56
q - 31 = 56
q
−
31
=
56
\newline
(B)
q
+
31
=
56
q + 31 = 56
q
+
31
=
56
Get tutor help
Leo and his friends are playing a new game called Pumpkin Patch. There are
p
p
p
pumpkin cards in total, and the goal of the game is to get them all. To start, Leo splits up the pumpkin cards evenly among the
5
5
5
players. He gives
10
10
10
pumpkin cards to each player.
\newline
Which diagram models the story?
\newline
Which equation models the story?
\newline
Choices:
\newline
(A)
p
5
=
10
\frac{p}{5} = 10
5
p
=
10
\newline
(B)
5
p
=
10
5p = 10
5
p
=
10
Get tutor help
Use the equation
d
=
y
+
5
d = y + 5
d
=
y
+
5
to find the value of
d
d
d
when
y
=
10
y = 10
y
=
10
.
\newline
d
=
d =
d
=
____
Get tutor help
The following graph, made by the manager of the basketball team, compares the free throw percentages for various players. A bar graph entitled Free Throw Percentages shows players on the
x
x
x
-axis and no label or numbers on the
y
y
y
-axis, but there are
6
6
6
horizontal lines. Player A is a blue bar that reaches just past the fourth line. Player B is a blue bar that reaches just past the fourth line. Player C is a blue bar that reaches halfway past the fourth line. Player D is a blue bar that reaches halfway past the fourth line. Player E is a blue bar that reaches just below the fifth line. Player F is a blue bar that almost touches the fifth line. Player G is a blue bar that reaches just past the fifth line. Player H is a red bar that reaches a quarter of the distance to the sixth line.
\newline
Which statement best describes why this graph could be misleading?
\newline
We don't know if all of the people on the team are included in the graph.
\newline
The graph does not indicate if the free throws were made at home or away.
\newline
The color of the bar for Player H is different from the color of the other bars in the graph.
\newline
The graph is missing the scale on the
y
y
y
-axis, making it unclear as to how much higher the free throw percentage is for one player than for another.
Get tutor help
Two equations are shown. Equation
1
1
1
:
2
3
(
x
−
6
)
=
6
\frac{2}{3}(x-6)=6
3
2
(
x
−
6
)
=
6
Equation
2
2
2
:
2
3
y
−
6
=
6
\frac{2}{3}y-6=6
3
2
y
−
6
=
6
Solve each equation. Then, enter a number in each box to make this statement true. The value of x is ◻ , and the value of y is ◻
Get tutor help
Use the equation
r
=
h
+
9
r = h + 9
r
=
h
+
9
to find the value of
r
r
r
when
h
=
3
h = 3
h
=
3
.
\newline
r
=
r =
r
=
____
Get tutor help
Use the equation
j
=
t
−
3
j = t - 3
j
=
t
−
3
to find the value of
j
j
j
when
t
=
5
t = 5
t
=
5
.
\newline
j
=
j =
j
=
____
Get tutor help
Use the equation
g
=
z
−
4
g = z - 4
g
=
z
−
4
to find the value of
g
g
g
when
z
=
5
z = 5
z
=
5
.
\newline
g
=
g =
g
=
____
Get tutor help
Use the equation
f
=
u
+
10
f = u + 10
f
=
u
+
10
to find the value of
f
f
f
when
u
=
6
u = 6
u
=
6
.
\newline
f
=
f =
f
=
____
Get tutor help
Use the equation
y
=
r
+
3
y = r + 3
y
=
r
+
3
to find the value of
y
y
y
when
r
=
2
r = 2
r
=
2
.
\newline
y
=
y =
y
=
____
Get tutor help
Use the equation
r
=
h
−
6
r = h - 6
r
=
h
−
6
to find the value of
r
r
r
when
h
=
7
h = 7
h
=
7
.
\newline
r
=
r =
r
=
____
Get tutor help
Use the equation
c
=
j
+
6
c = j + 6
c
=
j
+
6
to find the value of
c
c
c
when
j
=
6
j = 6
j
=
6
.
\newline
c
=
c =
c
=
____
Get tutor help
Use the equation
b
=
g
+
8
b = g + 8
b
=
g
+
8
to find the value of
b
b
b
when
g
=
1
g = 1
g
=
1
.
\newline
b
=
b =
b
=
____
Get tutor help
Use the equation
r
=
z
+
8
r = z + 8
r
=
z
+
8
to find the value of
r
r
r
when
z
=
9
z = 9
z
=
9
.
\newline
r
=
r =
r
=
____
Get tutor help
Use the equation
a
=
m
+
5
a = m + 5
a
=
m
+
5
to find the value of
a
a
a
when
m
=
10
m = 10
m
=
10
.
\newline
a
=
a =
a
=
____
Get tutor help
Use the equation
d
=
q
+
9
d = q + 9
d
=
q
+
9
to find the value of
d
d
d
when
q
=
10
q = 10
q
=
10
.
\newline
d
=
d =
d
=
____
Get tutor help
Use the equation
a
=
p
−
2
a = p - 2
a
=
p
−
2
to find the value of
a
a
a
when
p
=
4
p = 4
p
=
4
.
\newline
a
=
a =
a
=
____
Get tutor help
Use the equation
h
=
s
+
6
h = s + 6
h
=
s
+
6
to find the value of
h
h
h
when
s
=
8
s = 8
s
=
8
.
\newline
h
=
h =
h
=
____
Get tutor help
Use the equation
p
=
n
+
3
p = n + 3
p
=
n
+
3
to find the value of
p
p
p
when
n
=
7
n = 7
n
=
7
.
\newline
p
=
p =
p
=
____
Get tutor help
Use the equation
t
=
p
+
4
t = p + 4
t
=
p
+
4
to find the value of
t
t
t
when
p
=
5
p = 5
p
=
5
.
\newline
t
=
t =
t
=
____
Get tutor help
Use the equation
h
=
m
+
8
h = m + 8
h
=
m
+
8
to find the value of
h
h
h
when
m
=
7
m = 7
m
=
7
.
\newline
h
=
h =
h
=
____
Get tutor help
Use the equation
w
=
d
+
9
w = d + 9
w
=
d
+
9
to find the value of
w
w
w
when
d
=
1
d = 1
d
=
1
.
\newline
w
=
w =
w
=
____
Get tutor help
Use the equation
h
=
y
+
1
h = y + 1
h
=
y
+
1
to find the value of
h
h
h
when
y
=
1
y = 1
y
=
1
.
\newline
h
=
h =
h
=
____
Get tutor help
Use the equation
q
=
g
+
8
q = g + 8
q
=
g
+
8
to find the value of
q
q
q
when
g
=
2
g = 2
g
=
2
.
\newline
q
=
q =
q
=
____
Get tutor help
This equation shows how the time required to ring up a customer is related to the number of items being purchased.
\newline
t
=
p
+
9
t = p + 9
t
=
p
+
9
\newline
The variable
p
p
p
represents the number of items being purchased, and the variable
t
t
t
represents the time required to ring up the customer. How long does it take to ring up a customer with
5
5
5
items?
\newline
_____ seconds
Get tutor help
This equation shows how the accuracy of Dakota's watch is related to how long it's been since she last set it.
\newline
s
=
5
d
s = 5d
s
=
5
d
\newline
The variable
d
d
d
represents the number of days passed since Dakota last set her watch, and the variable
s
s
s
represents how many seconds behind the watch is. How far behind is Dakota's watch if she last set it
3
3
3
days ago?
\newline
_____ seconds
Get tutor help
This equation shows how the total cost of visiting the art museum as a member is related to the number of visits.
\newline
c
=
v
+
16
c = v + 16
c
=
v
+
16
\newline
The variable
v
v
v
represents the number of visits to the art museum, and the variable
c
c
c
represents the total cost of those visits. For a member of the art museum, what is the total cost of
2
2
2
visits?
\newline
$
\$
$
_____
Get tutor help
This equation shows how the number of pies Jonah can bake is related to the number of additional cups of sugar he buys.
\newline
p
=
s
+
11
p = s + 11
p
=
s
+
11
\newline
The variable
s
s
s
represents the number of additional cups of sugar Jonah buys, and the variable
p
p
p
represents the total number of pies he can bake. With
2
2
2
additional cups of sugar, how many total pies can Jonah bake?
\newline
_____ pies
Get tutor help
This equation shows how the total number of necklaces Krysta owns is related to the amount of money she spends on additional necklaces.
\newline
n
=
2
d
n = 2d
n
=
2
d
\newline
The variable
d
d
d
represents the amount of money she spends on additional necklaces, and the variable
n
n
n
represents the total number of necklaces she owns. With
$
1
\$1
$1
to spend on new necklaces, how many total necklaces can Krysta own?
\newline
_____ necklaces
Get tutor help
This equation shows how the number of flowers Lucia can have in her garden is related to the number of seed packets she purchases.
\newline
f
=
s
+
9
f = s + 9
f
=
s
+
9
\newline
The variable
s
s
s
represents the number of seed packets she purchases, and the variable
f
f
f
represents the total number of flowers in the garden. With
1
1
1
seed packet, how many total flowers can Lucia have in her garden?
\newline
_____ flowers
Get tutor help
This equation shows how the cost of a cab ride depends on the distance in miles.
\newline
c
=
d
+
5
c = d + 5
c
=
d
+
5
\newline
The variable
d
d
d
represents the number of miles driven, and the variable
c
c
c
represents the cost in dollars. If a cab ride is
5
5
5
miles long, how much will it cost?
\newline
$
\$
$
_____
Get tutor help
This equation shows how the total number of appetizer recipes Kimi knows depends on the number of weeks she attends culinary school.
\newline
a
=
w
+
13
a = w + 13
a
=
w
+
13
\newline
The variable
w
w
w
represents the number of weeks she has attended culinary school, and the variable
a
a
a
represents the total number of appetizer recipes she knows. After
4
4
4
weeks of culinary school, how many total appetizer recipes will Kimi know?
\newline
_____ appetizer recipes
Get tutor help
This equation shows how the total number of hair bands Sally owns is related to the amount of money she spends on additional hair bands.
\newline
h
=
6
d
h = 6d
h
=
6
d
\newline
The variable
d
d
d
represents the amount of money she spends on additional hair bands, and the variable
h
h
h
represents the total number of hair bands she owns. With
$
1
\$1
$1
to spend on new hair bands, how many total hair bands can Sally own?
\newline
_____ hair bands
Get tutor help
Dave and Buster's is running a promotion that they will give everyone in a school a free hour of play time. The school that has the most people sign up for alerts on the Dave and Buster's app will win the free time.
\newline
Saylesville has
364
364
364
students and
1
2
\frac{1}{2}
2
1
of the school signed up. Central has
385
385
385
students and
45
%
45\%
45%
of the school signed up. Northern has
510
510
510
students and
30
%
30\%
30%
of the school signed up. Lonsdale has
4
4
4
0
0
0
students and
\newline
4
4
4
1
1
1
of the school signed up.
\newline
Which school won the free hour of play time? Show all of your work to prove your answer. Round your answers to the nearest whole number, if needed.
Get tutor help
Audrey is reading a great book. The function
y
=
−
30
x
+
240
y = -30x + 240
y
=
−
30
x
+
240
represents the total number of pages Audrey has left,
y
y
y
, depending on how many hours she reads,
x
x
x
.
\newline
What is true about the function?
\newline
Choices:
\newline
(A)It is linear because it is always decreasing.
\newline
(B)It is linear because it decreases at a constant rate.
\newline
(C)It is nonlinear because it is always decreasing.
\newline
(D)It is nonlinear because it decreases at a constant rate.
Get tutor help
1
2
3
Next
