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Math Problems
Grade 7
Quantities that combine to zero: word problems
Nayeli lights a
4
m
2
4 \mathrm{~m}^{2}
4
m
2
space with
12
12
12
candles. Citlali lights a
10
m
2
10 \mathrm{~m}^{2}
10
m
2
space with
30
30
30
of the same type of candles.
\newline
Whose space is lit brighter?
\newline
Choose
1
1
1
answer:
\newline
(A) Nayeli's area
\newline
(B) Citlali's area
\newline
(C) The spaces are equally bright.
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Ari thinks the perfect milkshake has
5
5
5
scoops of ice cream for every
3
3
3
spoonfuls of caramel. Freeze Zone makes batches of milkshakes with
10
10
10
scoops of ice cream and
7
7
7
spoonfuls of caramel.
\newline
What will Ari think about the amount of caramel in Freeze Zone's milkshakes?
\newline
Choose
1
1
1
answer:
\newline
(A) Freeze Zone's milkshakes have too much caramel.
\newline
(B) Freeze Zone's milkshakes have too little caramel.
\newline
(C) Freeze Zone's milkshakes are just right.
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Abby is buying a rectangular widescreen TV that she will hang on the wall between two windows such that the longer side of the TV is horizontal. The windows are
36
36
36
inches apart horizontally, and a widescreen TV is approximately twice as wide as it is tall. Which of the following could be the diagonal length of a widescreen TV that fits between the windows?
\newline
Choose
1
1
1
answer:
\newline
(A)
32
32
32
inches
\newline
(B)
42
42
42
inches
\newline
(C)
55
55
55
inches
\newline
(D)
60
60
60
inches
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Derrick has
22
\mathbf{2 2}
22
dollars. Colleen has
x
x
x
dollars. Which of the following represents the total amount of money Derrick and Colleen have, in dollars?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
−
22
x-22
x
−
22
\newline
(B)
x
+
22
x+22
x
+
22
\newline
(C)
22
x
22 x
22
x
\newline
(D)
22
x
+
22
22 x+22
22
x
+
22
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We want to find the intersection points of the graphs given by the following system of equations:
\newline
{
x
−
y
=
−
4
y
=
5
(
x
+
1
)
2
−
3
\left\{\begin{array}{l} x-y=-4 \\ y=5(x+1)^{2}-3 \end{array}\right.
{
x
−
y
=
−
4
y
=
5
(
x
+
1
)
2
−
3
\newline
One of the intersection points is
(
−
2
,
2
)
(-2,2)
(
−
2
,
2
)
.
\newline
Find the other intersection point. Your answer must be exact.
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Aiden has
$
200
\$ 200
$200
with which to purchase hats and t-shirts that are to be sold at his class' next fundraiser. Each hat costs the same amount of money, and each t-shirt costs the same amount of money. If Aiden spends all his money entirely on hats, he will get
40
40
40
hats. If Aiden purchases only
t
t
t
-shirts, he will get
80
80
80
t
\mathrm{t}
t
-shirts. Which of the following best models the relationship between the number of hats,
h
h
h
, and the number of
t
\mathrm{t}
t
-shirts,
t
t
t
, that Aiden could purchase with this money?
\newline
Choose
1
1
1
answer:
\newline
(A)
40
h
+
80
t
=
400
40 h+80 t=400
40
h
+
80
t
=
400
\newline
(B)
80
h
+
40
t
=
200
80 h+40 t=200
80
h
+
40
t
=
200
\newline
(C)
5
h
+
2.5
t
=
200
5 h+2.5 t=200
5
h
+
2.5
t
=
200
\newline
(D)
2.5
h
+
5
t
=
200
2.5 h+5 t=200
2.5
h
+
5
t
=
200
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