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Math Problems
Grade 6
Identify independent and dependent variables: word problems
Susan manages the Wayne Orchard, which produces many different types of fruit, including pears. The more pear trees that have been planted in the orchard, the more barrels of pears the orchard will produce.
\newline
p
p
p
= 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
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
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A solar farm in California produces much of its output during the summer, when the sun is the most intense. The amount of power produced by a solar cell increases with the amount of sunlight it receives.
\newline
p
=
p =
p
=
the amount of power produced
\newline
s
=
s =
s
=
the amount of sunlight received
\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
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A solar farm in California produces much of its output during the summer, when the sun is the most intense. The more sunlight a solar cell receives, the more power it will produce.
\newline
s
s
s
= the amount of sunlight received
\newline
p
p
p
= the amount of power produced
\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
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Lillian 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 Lillian will need to wait
\newline
p
p
p
= the number of people in line ahead of Lillian
\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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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)
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
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Cora is making goodie bags for her child's birthday party, and she is buying bottles of bubbles for the bags. The number of party guests determines how many bottles of bubbles she will need to purchase.
\newline
g
=
g =
g
=
the number of guests
\newline
b
=
b =
b
=
the number of bottles of bubbles Cora purchases
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
b
b
b
is the independent variable and
g
g
g
is the dependent variable
\newline
(B)
g
g
g
is the independent variable and
b
b
b
is the dependent variable
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Adele runs the Boone Farm, which produces many different crops, including wheat. The number of bushels of wheat produced by the farm each year depends on the number of plots of land that are devoted to growing wheat.
\newline
w
=
w =
w
=
the number of bushels of wheat produced each year
\newline
p
=
p =
p
=
the number of plots of land devoted to growing wheat
\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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The organizers of a large rock concert must follow fire safety regulations regarding the capacity of the arena. The capacity determines the maximum number of tickets sold.
\newline
c
c
c
= the capacity of the arena
\newline
t
t
t
= the maximum number of tickets sold
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
t
t
t
is the independent variable and
c
c
c
is the dependent variable
\newline
(B)
c
c
c
is the independent variable and
t
t
t
is the dependent variable
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The manager of a restaurant decides how many servers to schedule for a particular night based upon how many reservations were made for that night.
\newline
s
=
s =
s
=
the number of servers scheduled to work
\newline
r
=
r =
r
=
the number of reservations
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
r
r
r
is the independent variable and
s
s
s
is the dependent variable
\newline
(B)
s
s
s
is the independent variable and
r
r
r
is the dependent variable
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Students at the Seaside High School homecoming dance always get their pictures taken. The number of pictures the photographer will take is determined by how many students are attending the dance.
\newline
p
=
p =
p
=
the number of pictures the photographer will take
\newline
s
=
s =
s
=
the number of students attending the dance
\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
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A committee is organizing a music festival in Cass County. The number of bands that will be able to play at the festival is determined by the amount of time that the venue has been reserved for.
\newline
b
=
b =
b
=
the number of bands that will be able to play
\newline
t
=
t =
t
=
the amount of time that the venue has been reserved for
\newline
Which of the variables is independent and which is dependent?
\newline
Choices:
\newline
(A)
b
b
b
is the independent variable and
t
t
t
is the dependent variable
\newline
(B)
t
t
t
is the independent variable and
b
b
b
is the dependent variable
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Sofia and Justine are preparing meals to serve at a local homeless shelter. The more meals they prepare, the more people they will be able serve.
\newline
m
m
m
= the number of meals Sofia and Justine prepare
\newline
p
p
p
= the number of people Sofia and Justine will be able to serve
\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
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Solve the system by substitution.
\newline
2
x
+
7
y
=
48
x
=
6
y
+
5
\begin{aligned} 2 x+7 y & =48 \\ x & =6 y+5 \end{aligned}
2
x
+
7
y
x
=
48
=
6
y
+
5
\newline
(
□
,
□
)
(\square, \square)
(
□
,
□
)
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Solve the system by substitution.
\newline
y
=
−
5
x
y
=
−
x
+
4
\begin{array}{l} y=-5 x \\ y=-x+4 \end{array}
y
=
−
5
x
y
=
−
x
+
4
\newline
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Solve the system by substitution.
\newline
−
6
x
−
5
y
=
−
8
y
=
−
2
x
\begin{aligned} -6 x-5 y & =-8 \\ y & =-2 x \end{aligned}
−
6
x
−
5
y
y
=
−
8
=
−
2
x
\newline
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
Solve the system by substitution.
\newline
y
=
−
2
x
y
=
5
x
+
7
\begin{array}{l} y=-2 x \\ y=5 x+7 \end{array}
y
=
−
2
x
y
=
5
x
+
7
\newline
(
□
,
□
)
(\square, \square)
(
□
,
□
)
Get tutor help
