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Math Problems
Grade 7
Write and solve equations for proportional relationships
Read the description of a proportional relationship.
\newline
Every few years, Russell's entire family gets together for a family reunion. This year, Russell's parents are hosting, and they have to cook a lot of food to feed the crowd. Russell has volunteered to do the most tedious job: shelling peas. There is a proportional relationship between the amount of time (in minutes) Russell spends shelling peas,
x
x
x
, and the weight (in pounds) of the peas he has shelled,
y
y
y
.
\newline
After
10
10
10
minutes, Russell has shelled
2
2
2
pounds of peas. Write the equation for the relationship between
x
x
x
and
y
y
y
.
\newline
y
=
_
_
y = \_\_
y
=
__
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Read the description of a proportional relationship.
\newline
Alan's class is having a holiday party, and he is in charge of bringing juice. He decides to bring powdered juice mix and add water to it at school. There is a proportional relationship between the volume of water Alan uses to make the juice (in liters),
x
x
x
, and the number of scoops of juice mix he uses,
y
y
y
.
\newline
To make the juice, Alan combines
4
4
4
liters of water and
12
12
12
scoops of juice mix. Write the equation for the relationship between
x
x
x
and
y
y
y
.
\newline
y
=
_
y = \_
y
=
_
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Read the description of a proportional relationship.
\newline
Every few years, Kenny's entire family gets together for a family reunion. This year, Kenny's parents are hosting, and they have to cook a lot of food to feed the crowd. Kenny has volunteered to do the most tedious job: shelling peas. There is a proportional relationship between the amount of time (in minutes) Kenny spends shelling peas,
x
x
x
, and the weight (in pounds) of the peas he has shelled,
y
y
y
.
\newline
After
6
6
6
minutes, Kenny has shelled
3
3
3
pounds of peas. Write the equation for the relationship between
x
x
x
and
y
y
y
.
\newline
y
=
_
_
y = \_\_
y
=
__
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Read the description of a proportional relationship.
\newline
As a young girl, Nicole enjoyed watching her father make things in his woodworking shop. Now that she's grown up, Nicole builds wooden furniture for a living. Her most popular product is a cedar porch swing. There is a proportional relationship between the time (in days) Nicole spends making porch swings,
x
x
x
, and the number of swings she builds,
y
y
y
.
\newline
It takes Nicole
10
10
10
days to build
8
8
8
swings. Write the equation for the relationship between
x
x
x
and
y
y
y
.
\newline
y
=
_
y = \_
y
=
_
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Read the description of a proportional relationship.
\newline
Scarlett wants to save up some money to buy a new smartphone, so she babysits on the weekends. There is a proportional relationship between the time Scarlett spends babysitting (in hours),
x
x
x
, and the amount of money she earns babysitting (in dollars),
y
y
y
.
\newline
For
1
1
1
hour of babysitting, Scarlett earns
$
6
\$6
$6
. Write the equation for the relationship between
x
x
x
and
y
y
y
.
\newline
y
=
y =
y
=
____
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Read the description of a proportional relationship.
\newline
Anthony has written his own recipe for pot roast. There is a proportional relationship between the weight (in pounds) of the pot roast,
x
x
x
, and the total cooking time (in hours),
y
y
y
.
\newline
His recipe says that a
5
5
5
-pound roast should take
2
2
2
hours to cook. Write the equation for the relationship between
x
x
x
and
y
y
y
.
\newline
y
=
_
y = \_
y
=
_
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Read the description of a proportional relationship.
\newline
Kurt owns and operates Stain-B-Gone Carpet Cleaners. He uses a special non-toxic cleaning solution to clean carpets. There is a proportional relationship between the amount of cleaning solution (in quarts) Kurt uses,
x
x
x
, and the area of carpet (in square yards) he cleans with the solution,
y
y
y
.
\newline
Kurt uses
4
4
4
quarts of cleaning solution to clean
12
12
12
square yards of carpet. Write the equation for the relationship between
x
x
x
and
y
y
y
.
\newline
y
=
_
y = \_
y
=
_
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Bryce is an electrician. He charges a service fee to visit a job site as well as an hourly rate for his labor. The graph shows the linear relationship between the total amount Bryce charges and the number of hours he spends on a job.
\newline
\newline
What hourly rate does Bryce charge for his labor?
\newline
$
\$
$
____ per hour
\newline
Complete the equation to represent the relationship between the total amount Bryce charges in dollars,
T
T
T
, and the total number of hours he spends on a job,
h
h
h
.
\newline
T = ____ h + ____
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The staff at an aquarium drained a full squid tank in order to clean it. There is a linear relationship between the number of hours the squid tank has been draining and the volume of water remaining in the tank. The graph shows the volume of water in the tank as time passes.
\newline
What is the capacity of the squid tank?
\newline
_
_
_
\_\_\_
___
gallons
\newline
Complete the equation to represent the relationship between the number of gallons remaining in the squid tank,
V
V
V
, and the elapsed time,
t
t
t
.
\newline
V
=
_
_
_
_
t
+
_
_
_
V = \_\_\_\_ t + \_\_\_
V
=
____
t
+
___
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Example Stem
2
2
2
: A punch recipe calls for
3
3
3
cups of orange juice for every
2
2
2
cups of cranberry juice.
\newline
Select all of the statements about the recipe that are correct.
\newline
A. There are
3
3
3
cups of orange juice for every
5
5
5
cups of punch.
\newline
B. The ratio of cranberry juice to orange juice is
2
2
2
to
3
3
3
.
\newline
C. The ratio of orange juice to cranberry juice is
2
:
1
2: 1
2
:
1
.
\newline
D. The ratio of cranberry juice to punch is
2
:
5
2: 5
2
:
5
.
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The results of a survey asking teens their favorite type of book to read is shown.
\newline
7
7
7
. Out of
250
250
250
teens, predict how many would choose mystery as their favorite type of book to read.
\newline
8
8
8
. Out of
250
250
250
teens, predict how many would choose adventure as their favorite type of book to read.
\newline
9
9
9
. Out of
250
250
250
teens, predict how many would choose romance as their favorite type of book to read.
\newline
Look at the graph
\newline
Favorite Type of Book
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A lake near the Arctic Circle is covered by a
2
2
2
-meter-thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate. After
3
3
3
weeks, the sheet is only
1.25
1.25
1.25
meters thick. Complete the equation for the relationship between the thickness and number of weeks.
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A team of geologists creates a borehole to record the temperature, in degrees Fahrenheit, is recorded along with the depth, in kilometers, in the table. Which of the following best explains the relationship between
T
T
T
and
d
d
d
?
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Carbon dating involves the measurement of the amount of carbon-
\newline
14
14
14
in a sample. Archaeologists sometimes use carbon dating to estimate the number of years since an organism died. The function shows the ratio,
R
(
t
)
R(t)
R
(
t
)
, of carbon-
\newline
14
14
14
remaining in a sample to the original amount of carbon-
\newline
14
14
14
after
t
t
t
years. If one sample was
3
3
3
times as old as another sample of the same material, how would the carbon-
\newline
14
14
14
ratios of the samples relate? Choose
1
1
1
answer:
\newline
(Choice A) The ratio of the older sample would be
3
3
3
times the ratio of the newer sample.
\newline
(Choice B) The ratio of the newer sample would be
3
3
3
times the ratio of the older sample.
\newline
(Choice C) The ratio of the older sample would be the cube of the ratio of the newer sample.
\newline
(Choice D) The ratio of the newer sample would be the cube of the ratio of the older sample.
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The weights of
9
9
9
different cats, in pounds, were used to create the box plot above. Which of the numbers below is the range of the set of weights?
\newline
A.
7
7
7
\newline
B.
3
3
3
\newline
C.
1.5
1.5
1.5
\newline
D.
11
11
11
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At the beginning of the season, MacDonald had to remove
5
5
5
orange trees from his farm. Each of the remaining trees produced
210
210
210
oranges for a total harvest of
41
,
790
41,790
41
,
790
oranges. If
t
t
t
is the initial number of trees on MacDonald's farm, which of the following equations best describes the situation?
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0.30
P
+
0.25
G
=
57
0.30 P+0.25 G=57
0.30
P
+
0.25
G
=
57
\newline
A homeowner uses
G
G
G
hours of natural gas heat and
P
P
P
hours of heat from a pellet stove to heat her house one month, with a total of
57
57
57
therms of output. How many therms per hour does the pellet stove output?
\newline
□
\square
□
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