Unit 8: Using Equations to Solve Problems
END-OF-UNIT ASSESSMENT
Name: _________________
Date: __________ Period: ___
Teacher: ________________
Read the following statement before answering Problems 1, 2, and 3.
Posting the Newsletter
Maria and Tony publish a monthly newsletter with 600 subscribers. In some months there is
not much news, and the newsletter is quite small. In other months, when sports or arts sections
are big, the newsletter runs to quite a large number of pages. The cost of producing the
newsletter is a problem, and Maria and Tony have been asked to investigate how much it costs
to mail out the newsletter and whether these costs can be reduced.
The First-Class postage charge depends on the weight of the newsletter, provided the weight
does not exceed 13 ounces. The envelope weighs 0.5 ounces but the total weight depends on
the number of sheets of paper needed for each newsletter. Maria and Tony currently use a
high-quality paper, although two grades of lighter paper are available.
1. Using less than 20 of your own words, write a description of the problem.
2. Which quantities in the situation are constants?
3. Which quantities in the situation are variables?
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End-of-Unit Assessment
4. The paper that Maria and Tony use is called “28-pound paper,” since 1000 sheets of this
paper weigh 28 pounds. Use this information to complete the following table for the
weights of different sized newsletters. (Include the weight of the envelope.)
Number of sheets
0
x
5
10
15
20
25
Weight of newsletter
(w oz)
a. Find the equation for this relationship.
b. What is the largest size newsletter that could be mailed at First-Class postage rates?
5. Tony and Maria have the following graph for the First-Class postage charges.
y
3.00
2.50
Cost ($)
2.00
1.50
1.00
0.50
w
0
0
1
2
3
4
5
6
7
8
Weight (ounces)
9
10
11
12
13
a. Give the coordinates of the two points marked with the larger dots.
b. Find the equation for the relationship between y and w.
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End-of-Unit Assessment
6. a. What would be the postage charge for a newsletter of 10 sheets?
b. On the graph provided below, plot the relationship between the number of sheets in the
newsletter and the postage charge, y dollars.
c. On this same set of axes sketch two more graphs, the ones that would apply if Maria and
Tony used lighter paper for their newsletter—either 24-pound paper or 20-pound paper.
y
3.00
2.80
2.60
2.40
2.20
2.00
Cost ($)
1.80
1.60
1.40
1.20
1.00
0.80
0.60
0.40
0.20
x
0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
Number of Sheets
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385
End-of-Unit Assessment
7. Write a short report about how postage costs for the newsletter could be kept to no more
than $2.00 and how Tony and Maria could compare costs for using the different types
of paper.
Your report should take into account that fact that post office scales measure weights in
whole numbers of ounces.
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End-of-Unit Assessment: Page 4 of 4
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