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Math Problems
Grade 7
Identify independent and dependent variables
A wind farm in California produces much of its output during the summer, when the winds are fastest. The amount of power produced depends on the average wind speed.
\newline
p
=
p =
p
=
the amount of power produced
\newline
w
=
w =
w
=
the average wind speed
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
p
p
p
is the independent variable and
w
w
w
is the dependent variable
\newline
(B)
w
w
w
is the independent variable and
p
p
p
is the dependent variable
Get tutor help
At a deli counter, the weight of a customer's order determines the price.
\newline
w
=
w =
w
=
the weight
\newline
p
=
p =
p
=
the price
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
w
w
w
is the independent variable and
p
p
p
is the dependent variable
\newline
(B)
p
p
p
is the independent variable and
w
w
w
is the dependent variable
Get tutor help
Antonio manages the Lawrence Orchard, which produces many different types of fruit, including pears. The number of barrels of pears the orchard will produce depends on the number of pear trees that have been planted in the orchard.
\newline
b
=
b =
b
=
the number of barrels of pears the orchard will produce
\newline
p
=
p =
p
=
the number of pear trees that have been planted in the orchard
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
b
b
b
is the independent variable and
p
p
p
is the dependent variable
\newline
(B)
p
p
p
is the independent variable and
b
b
b
is the dependent variable
Get tutor help
Students at the Lexington High School homecoming dance always get their pictures taken. The more students there are at the dance, the more pictures the photographer will take.
\newline
s
=
s =
s
=
the number of students attending the dance
\newline
p
=
p =
p
=
the number of pictures the photographer will take
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
s
s
s
is the independent variable and
p
p
p
is the dependent variable
\newline
(B)
p
p
p
is the independent variable and
s
s
s
is the dependent variable
Get tutor help
Hakim is planning a scavenger hunt for his friends. The number of friends taking part determines how many teams there will be.
\newline
f
=
f =
f
=
the number of friends
\newline
t
=
t =
t
=
the number of teams
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
f
f
f
is the independent variable and
t
t
t
is the dependent variable
\newline
(B)
t
t
t
is the independent variable and
f
f
f
is the dependent variable
Get tutor help
Matt brings reusable shopping bags from home whenever he goes to the store. The number of products on his shopping list influences how many reusable bags he brings to the store.
\newline
p
p
p
= the number of products on Matt's shopping list
\newline
b
b
b
= the number of bags Matt brings to the store
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
p
p
p
is the independent variable and
b
b
b
is the dependent variable
\newline
(B)
b
b
b
is the independent variable and
p
p
p
is the dependent variable
Get tutor help
Jim and his friends are at an arcade and are redeeming their tickets for prizes. The number of tickets they have won determines how many prizes they can get.
\newline
t
=
t =
t
=
the number of tickets the friends have won
\newline
p
=
p =
p
=
the number of prizes the friends can get
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
p
p
p
is the independent variable and
t
t
t
is the dependent variable
\newline
(B)
t
t
t
is the independent variable and
p
p
p
is the dependent variable
Get tutor help
Jake and Kendall work at a small film studio and are planning a screening of their first feature-length film. The number of seats they will need to set up in the screening room depends on the number of people who attend the screening.
\newline
s
=
s =
s
=
the number of seats Jake and Kendall will need to set up
\newline
p
=
p =
p
=
the number of people who attend the screening
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
p
p
p
is the independent variable and
s
s
s
is the dependent variable
\newline
(B)
s
s
s
is the independent variable and
p
p
p
is the dependent variable
Get tutor help
At a conference, Cole is handing out candy to people who visit his booth. The number of visitors determines the total amount of candy he hands out.
\newline
c
=
c =
c
=
the total amount of candy Cole hands out
\newline
v
=
v =
v
=
the number of visitors to Cole's booth
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
c
c
c
is the independent variable and
v
v
v
is the dependent variable
\newline
(B)
v
v
v
is the independent variable and
c
c
c
is the dependent variable
Get tutor help
A team from the Department of Public Works is painting lines on the freeway. The number of hours needed to finish the project depends on the length of road that needs to be lined.
\newline
h
=
h =
h
=
the number of hours needed
\newline
r
=
r =
r
=
the length of road
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
r
r
r
is the independent variable and
h
h
h
is the dependent variable
\newline
(B)
h
h
h
is the independent variable and
r
r
r
is the dependent variable
Get tutor help
Ivan is a member of the football team at his high school. The night before a game, the players enjoy a team dinner provided by their parents. Ivan's mom is making marshmallow treats for dessert. The number of players on the team determines how many treats she will make.
\newline
p
=
p =
p
=
the number of players on the football team
\newline
m
=
m =
m
=
the number of marshmallow treats Ivan's mom makes
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
p
p
p
is the independent variable and
m
m
m
is the dependent variable
\newline
(B)
m
m
m
is the independent variable and
p
p
p
is the dependent variable
Get tutor help
Sebastian is buying birthday candles for his grandmother's birthday cake. Her age, in years, will determine how many boxes of candles Sebastian will purchase.
\newline
y
=
y =
y
=
Sebastian's grandmother's age, in years
\newline
b
=
b =
b
=
how many boxes of candles Sebastian will purchase
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
y
y
y
is the independent variable and
b
b
b
is the dependent variable
\newline
(B)
b
b
b
is the independent variable and
y
y
y
is the dependent variable
Get tutor help
In the United States House of Representatives, the population of a state is used to calculate how many Representatives are from that state.
\newline
p
=
p =
p
=
the population of a state
\newline
r
=
r =
r
=
the number of Representatives
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
p
p
p
is the independent variable and
r
r
r
is the dependent variable
\newline
(B)
r
r
r
is the independent variable and
p
p
p
is the dependent variable
Get tutor help
In order to earn extra money during the summer, Trevor is working as a house painter. The amount of money he earns depends on the number of houses he paints.
\newline
m
=
m =
m
=
the amount of money Trevor earns
\newline
h
=
h =
h
=
the number of houses Trevor paints
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
m
m
m
is the independent variable and
h
h
h
is the dependent variable
\newline
(B)
h
h
h
is the independent variable and
m
m
m
is the dependent variable
Get tutor help
Gavin is a member of the football team at his high school. The night before a game, the players enjoy a team dinner provided by their parents. Gavin's mom is making marshmallow treats for dessert. The number of players on the team determines how many treats she will make.
\newline
p
=
p =
p
=
the number of players on the football team
\newline
m
=
m =
m
=
the number of marshmallow treats Gavin's mom makes
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
p
p
p
is the independent variable and
m
m
m
is the dependent variable
\newline
(B)
m
m
m
is the independent variable and
p
p
p
is the dependent variable
Get tutor help
Doug, a pastry chef, is designing a cake for a retirement party. The number of tiers on the cake will be based on how many guests are expected to attend the party.
\newline
t
=
t =
t
=
the number of tiers the cake will have
\newline
g
=
g =
g
=
the number of guests expected
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
g
g
g
is the independent variable and
t
t
t
is the dependent variable
\newline
(B)
t
t
t
is the independent variable and
g
g
g
is the dependent variable
Get tutor help
Mona is designing programs for her daughter's high school graduation. The number of pages in each program is dictated by the number of graduates.
\newline
p
=
p =
p
=
the number of pages in each program
\newline
g
=
g =
g
=
the number of graduates
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
g
g
g
is the independent variable and
p
p
p
is the dependent variable
\newline
(B)
p
p
p
is the independent variable and
g
g
g
is the dependent variable
Get tutor help
Karen is renting buses for a school field trip. The number of buses needed depends on how many students are going on the trip.
\newline
b
=
b =
b
=
the number of buses needed
\newline
s
=
s =
s
=
the number of students going on the trip
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(
A
)
(A)
(
A
)
b
b
b
is the independent variable and
s
s
s
is the dependent variable
\newline
(
B
)
(B)
(
B
)
s
s
s
is the independent variable and
b
b
b
is the dependent variable
Get tutor help
Tina manages the Scott Orchard, which produces many different types of fruit, including pears. The number of barrels of pears the orchard will produce depends on the number of pear trees that have been planted in the orchard.
\newline
b
=
b =
b
=
the number of barrels of pears the orchard will produce
\newline
p
=
p =
p
=
the number of pear trees that have been planted in the orchard
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
b
b
b
is the independent variable and
p
p
p
is the dependent variable
\newline
(B)
p
p
p
is the independent variable and
b
b
b
is the dependent variable
Get tutor help
Lacey works as a server at the Butler Restaurant. The amount of money she earns during a shift depends on the number of tables she serves.
\newline
m
=
m =
m
=
the amount of money Lacey earns
\newline
t
=
t =
t
=
the number of tables Lacey serves
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
m
m
m
is the independent variable and
t
t
t
is the dependent variable
\newline
(B)
t
t
t
is the independent variable and
m
m
m
is the dependent variable
Get tutor help
Susan and Hunter are raising money to purchase books for their school's library. The more money they raise, the more books they will be able to purchase for the library.
\newline
m
m
m
= the amount of money Susan and Hunter raise
\newline
b
b
b
= the number of books Susan and Hunter will be able to purchase
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
b
b
b
is the independent variable and
m
m
m
is the dependent variable
\newline
(B)
m
m
m
is the independent variable and
b
b
b
is the dependent variable
Get tutor help
Myra is planning a birthday party and plans to serve cupcakes. The number of cupcakes she will prepare depends on the number of her friends who plan to attend the party.
\newline
c
c
c
= the number of cupcakes Myra will prepare
\newline
f
f
f
= the number of Myra's friends who plan to attend the party
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
f
f
f
is the independent variable and
c
c
c
is the dependent variable
\newline
(B)
c
c
c
is the independent variable and
f
f
f
is the dependent variable
Get tutor help
Edmond is making sandwiches for a family picnic. The amount of bread he has determines how many sandwiches he can make.
\newline
b
b
b
= the amount of bread Edmond has
\newline
s
s
s
= the number of sandwiches Edmond can make
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
b
b
b
is the independent variable and
s
s
s
is the dependent variable
\newline
(B)
s
s
s
is the independent variable and
b
b
b
is the dependent variable
Get tutor help
Natalie is taking a standardized test. Her final test score will depend on the number of questions she answers correctly.
\newline
s
=
s =
s
=
Natalie's final test score
\newline
q
=
q =
q
=
the number of questions Natalie answers correctly
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
s
s
s
is the independent variable and
q
q
q
is the dependent variable
\newline
(B)
q
q
q
is the independent variable and
s
s
s
is the dependent variable
Get tutor help
Larry is assembling prize baskets for a raffle. The number of baskets he puts together depends on how many prizes were donated.
\newline
b
b
b
= the number of baskets Larry makes
\newline
p
p
p
= the number of prizes donated
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
b
b
b
is the independent variable and
p
p
p
is the dependent variable
\newline
(B)
p
p
p
is the independent variable and
b
b
b
is the dependent variable
Get tutor help
Wyatt and Neil are going hiking and are trying to figure out how much water they should bring with them on the hike. The amount of water they should bring depends on how long they plan to hike.
\newline
w
w
w
= the amount of water they should bring on the hike
\newline
t
t
t
= the length of the hike
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
w
w
w
is the independent variable and
t
t
t
is the dependent variable
\newline
(B)
t
t
t
is the independent variable and
w
w
w
is the dependent variable
Get tutor help
Becky is organizing a martial arts tournament and is ordering trophies for the winners. The more divisions there are in the tournament, the more trophies Becky needs to order.
\newline
d
=
d =
d
=
the number of divisions in the tournament
\newline
t
=
t =
t
=
the number of trophies Becky orders
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
d
d
d
is the independent variable and
t
t
t
is the dependent variable
\newline
(B)
t
t
t
is the independent variable and
d
d
d
is the dependent variable
Get tutor help
Oscar is a member of the football team at his high school. The night before a game, the players enjoy a team dinner provided by their parents. Oscar's mom is making marshmallow treats for dessert. The number of players on the team determines how many treats she will make.
\newline
p
=
p =
p
=
the number of players on the football team
\newline
m
=
m =
m
=
the number of marshmallow treats Oscar's mom makes
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
p
p
p
is the independent variable and
m
m
m
is the dependent variable
\newline
(B)
m
m
m
is the independent variable and
p
p
p
is the dependent variable
Get tutor help
Customers of the water company are billed based on consumption. The billing amount is determined by the amount of water consumed.
\newline
b
b
b
= the billing amount
\newline
w
w
w
= the amount of water consumed
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
b
b
b
is the independent variable and
w
w
w
is the dependent variable
\newline
(B)
w
w
w
is the independent variable and
b
b
b
is the dependent variable
Get tutor help
Darren and Naomi are going on a road trip together. They have a limited budget, so they consider several different routes and calculate the cost of gas for each route. The cost of gas for each route depends on the length of the route.
\newline
g
g
g
= the cost of gas
\newline
r
r
r
= the length of the route
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
g
g
g
is the independent variable and
r
r
r
is the dependent variable
\newline
(B)
r
r
r
is the independent variable and
g
g
g
is the dependent variable
Get tutor help
Mr. Malone is getting history textbooks for his class from a school storeroom. The number of students in the class determines how many books he gets.
\newline
s
=
s =
s
=
the number of students in Mr. Malone's class
\newline
t
=
t =
t
=
the number of history textbooks Mr. Malone gets from the storeroom
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
s
s
s
is the independent variable and
t
t
t
is the dependent variable
\newline
(B)
t
t
t
is the independent variable and
s
s
s
is the dependent variable
Get tutor help
Jessica is purchasing tickets to go on rides at the Union County Fair. The number of rides she can go on is dictated by how many tickets she purchases.
\newline
r
=
r =
r
=
the number of rides Jessica can go on
\newline
t
=
t =
t
=
the number of tickets Jessica purchases
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
r
r
r
is the independent variable and
t
t
t
is the dependent variable
\newline
(B)
t
t
t
is the independent variable and
r
r
r
is the dependent variable
Get tutor help
Trudy harvests mushrooms in the forests of Oregon and then sells them to local restaurant chefs. The value of the mushrooms depends on their weight.
\newline
v
=
v =
v
=
the value of the mushrooms
\newline
w
=
w =
w
=
the weight of the mushrooms
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
w
w
w
is the independent variable and
v
v
v
is the dependent variable
\newline
(B)
v
v
v
is the independent variable and
w
w
w
is the dependent variable
Get tutor help
Savannah, a florist, is assembling bouquets of roses to sell at her flower shop. The number of bouquets she can assemble depends on how many roses are in her shop.
\newline
b
b
b
= the number of bouquets Savannah can assemble
\newline
r
r
r
= the number of roses in the flower shop
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
r
r
r
is the independent variable and
b
b
b
is the dependent variable
\newline
(B)
b
b
b
is the independent variable and
r
r
r
is the dependent variable
Get tutor help
Troy is planning a picnic for his coworkers and plans to serve veggie burgers. The more of his coworkers who attend the picnic, the more veggie burgers he will prepare.
\newline
c
c
c
= the number of Troy's coworkers who attend the picnic
\newline
v
v
v
= the number of veggie burgers Troy prepares
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
c
c
c
is the independent variable and
v
v
v
is the dependent variable
\newline
(B)
v
v
v
is the independent variable and
c
c
c
is the dependent variable
Get tutor help
Ashley baked a pan of brownies for a potluck. The number of squares she cuts the brownies into will depend on the number of people attending the potluck.
\newline
s
=
s =
s
=
the number of squares Ashley cuts the brownies into
\newline
p
=
p =
p
=
the number of people attending the potluck
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
s
s
s
is the independent variable and
p
p
p
is the dependent variable
\newline
(B)
p
p
p
is the independent variable and
s
s
s
is the dependent variable
Get tutor help
Mia and Preston are baking cookies to sell at their school's bake sale. The more cookies they bake, the more money they will be able to raise for their school.
\newline
c
c
c
= the number of cookies they bake
\newline
m
m
m
= the amount of money they will be able to raise
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
c
c
c
is the independent variable and
m
m
m
is the dependent variable
\newline
(B)
m
m
m
is the independent variable and
c
c
c
is the dependent variable
Get tutor help
Grace is planning her wedding. The number of announcements she orders is determined by how many guests she wants to invite.
\newline
a
=
a =
a
=
the number of announcements
\newline
g
=
g =
g
=
the number of guests
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
g
g
g
is the independent variable and
a
a
a
is the dependent variable
\newline
(B)
a
a
a
is the independent variable and
g
g
g
is the dependent variable
Get tutor help
Harper works for a small company that sells books online and is responsible for mailing out the books to customers. Every morning she gets in line at the local post office and estimates the length of her wait. The length of her wait depends on the number of people in line ahead of her.
\newline
w
w
w
= the length of time Harper will need to wait
\newline
p
p
p
= the number of people in line ahead of Harper
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
w
w
w
is the independent variable and
p
p
p
is the dependent variable
\newline
(B)
p
p
p
is the independent variable and
w
w
w
is the dependent variable
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Which of these strategies would eliminate a variable in the system of equations?
\newline
{
2
x
+
8
y
=
−
3
3
x
+
6
y
=
−
4
\begin{cases} 2x+8y=-3 \ 3x+6y=-4 \end{cases}
{
2
x
+
8
y
=
−
3
3
x
+
6
y
=
−
4
\newline
Choose
2
2
2
answers:
\newline
A Multiply the top equation by
3
3
3
, multiply the bottom equation by
−
2
-2
−
2
, then add the equations.
\newline
B Multiply the top equation by
3
3
3
, multiply the bottom equation by
4
4
4
, then subtract the bottom equation from the top equation.
\newline
C Multiply the top equation by
−
4
-4
−
4
, multiply the bottom equation by
3
3
3
, then add the equations.
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