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Learning Math Home
Patterns, Functions, and Algebra
 
Session 8 Part A Part B Part C Homework
 
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Session 8, Part B:
Inverse Proportions

In This Part: Splitting a Prize | Ms. Anwar's Backyard | Another Inverse Porportion

Ms. Anwar is considering renting a house that has a large rectangular backyard. She wants to figure out if there will be room for her children's play equipment. The owner told her, "The backyard has an area of 2,000 square feet." Ms. Anwar thought about what he said and tried to imagine what the actual dimensions of the yard might be.

Problem B4

  

Fill in the table below to show some possibilities for the dimensions of the yard if the area is 2,000 square feet.

 

Length

 

Width

 

Area = length * width

50

 

40

 

2000

25

 

 

2000

100

 

 

2000

 

2

 

2000

 

 

2000

 

 

2000

 

 

2000

 

 

2000

 
show answers
 
 
 

Length

 

Width

 

Area = length * width

50

 

40

 

2000

25

 

80

 

2000

100

 

20

 

2000

1,000

 

2

 

2000

40

 

50

 

2000

80

 

25

 

2000

2000

 

1

 

2000

0.5

 

4000

 

2000

 

hide answers

 

 

Problem B5

Solution  

Find an equation relating the length (x) and the width (y) in the table above.


 

Problem B6

Solution  

Graph the length vs. width in the table above.


 

Problem B7

  

As x changes, what happens to y? Try to describe this relationship as clearly as possible. These problems may help you:
Note 6

a. 

Complete the table below. Round values for y to one decimal place, or use the exact fractional value.

 

x

 

y

 

Decrease
in y

20

 

100

 

--

30

 

66.7

 

33.3

40

 

 

50

 

 

60

 

 

70

 

 

80

 

 

90

 

 

100

 

 

 
show answers
 
 
 

x

 

y

 

Decrease in y

20

 

100

 

--

30

 

66.7

 

33.3

40

 

50

 

16.7

50

 

40

 

10

60

 

33.3

 

6.7

70

 

28.6

 

4.7

80

 

25

 

3.6

90

 

22.2

 

2.8

100

 

20

 

2.2

 

hide answers

 

b. 

As x increases by 10, what happens to y? Does y go up a fixed amount? An increasing amount? A decreasing amount?

c. 

As x doubles, what happens to y? As x triples, what happens to y?

d. 

If x is very small, what can you say about y? What if x is very big?


 

"Ms. Anwar's Backyard" problem taken from IMPACT Mathematics Course 3, developed by Education Development Center, Inc. (New York: Glencoe/McGraw-Hill, 2000), p.110. www.glencoe.com/sec/math

Next > Part B (Continued): Another Inverse Proportion

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