Aims Grade 8 Mathematics Sample Test And Think-Throughs With Answers Page 16
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36December 2009
A tower is 160 feet tall and casts a shadow 34 feet long. A person standing next to the
5
tower casts a shadow 1.5 feet long. Which equation will find the height of the person, x?
160
1.5
=
A
34
x
34
x
=
B
160
1.5
1.5x = 34 • 160
C
34x = 1.5 • 160
D
I notice that this problem is asking me to find an equation, not an answer. And, I see that all of the
answer options are equations since they have equals signs, so I need to set up a problem for
myself as if I were going to find the answer.
I will draw a picture with the measurements to help me better visualize this problem.
160 feet
?
34 feet
1.5 feet
Now that I see what I have, it looks like I need to create a proportion. Since I know the height of
the tower and the length of its shadow, that will be my first proportion.
Tower proportion
160 feet to 34 feet or 160 actual height
34 shadow length
My next proportion will be for the person. Since I do not know the height of the person, I will call
that x. I need to set up the proportion the same way as my first proportion, with the actual height
as the numerator and the shadow length as the denominator.
Person proportion
x feet to 1.5 feet or x actual height
1.5 shadow length
Since the problem is asking for an equation, I will set my proportions equal to each other.
Actual height
160
x
=
Shadow length
34
1.5
(continued on page 17)
Arizona Department of Education
16
Grade 8
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