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Math Problems
Grade 7
Quantities that combine to zero: word problems
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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