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Math Problems
Grade 7
Write and solve equations for proportional relationships
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. Write an equation to describe this situation.
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Two classmates have decided to read all the volumes in a popular series of books. Amy has already read
10
10
10
volumes and will continue to read new ones at a rate of
1
1
1
volume per week. Beth, who hasn't started reading the series yet, will read
3
3
3
volumes per week. At some point, Beth will catch up with Amy and they will be reading the same book. How many volumes will each girl have read by then?
\newline
Write a system of equations, graph them, and type the solution.
\newline
____ volumes
\newline
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Read the description of a proportional relationship.
\newline
Luther is starting a summer camp for children who are deaf or hard of hearing. He needs to hire enough counselors to chaperone the children. There is a proportional relationship between the number of counselors Luther hires,
x
x
x
, and the maximum number of children who can attend the camp,
y
y
y
.
\newline
By law, if Luther hires
2
2
2
counselors, then at most
10
10
10
children can attend the camp. 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
Tom and his friends set out to sea on their annual fishing trip. There is a proportional relationship between the time (in hours) Tom and his friends spend sailing,
x
x
x
, and their distance from shore (in miles),
y
y
y
.
\newline
After sailing for
1
1
1
hour, they are
5
5
5
miles from shore. 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
After a shipwreck, Vivian is stranded on a desert island. She needs to build a shelter, so she makes an axe using materials from the wreckage and starts cutting down trees. There is a proportional relationship between the number of days Vivian is stranded on the island,
x
x
x
, and the total number of trees she cuts down,
y
y
y
.
\newline
In her first
2
2
2
days on the island, Vivian cuts down a total of
6
6
6
trees. 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
Roxanne is measuring the diameter and the radius of different-sized circles. There is a proportional relationship between the radius of the circle in inches,
x
x
x
, and the diameter of the circle in inches,
y
y
y
.
\newline
A circle with a
3
3
3
-inch radius has a diameter of
6
6
6
inches. 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
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
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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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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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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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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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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