# Math0075 910 practice assignment 16 c

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Foundations of Mathematical Reasoning Version 3.0 (2020)
Student Pages
Copyright © 2020, The Charles A. Dana Center at The University of Texas at Austin
Practice Assignment 16.C
1) Two servers at a restaurant start their work shift just as a banquet is being
prepared. The number of plates that has been prepared for serving after a certain
number of minutes has passed is shown in the table below.
𝑥 = number of minutes that
have passed
2
3
8
𝑦 = number of plates prepared
32
38
68
Part A: Look at the first two data points in the table. What do they tell you about the
slope of the relationship between the number of minutes that have passed
relationship. Be specific and be sure to include units.
6 plates were served within the second and third minute.
Part B: Calculate the slope using the second and third data points from the table.
What does the slope tell you?
Slope is 6. (30/5)
Which means 6 plates per minute within 3rd and 8th minutes.
Part C: How does your response to Part B compare to Part A?
Both slopes are equal.
Part D: Calculate the slope for the first and third points.
Slope is 36/6 = 6
Which means 6 plates per minute within 2nd and 8th minutes.
Part E: Do you have enough information to predict the time for preparing 18
plates? Explain.
This shows a constant slope. Therefore, time taken to prepare 18
plates will be 3 minutes.
2) A cable company charges \$130 for digital cable and internet service. It charges
\$160 for digital cable, Internet service, and three premium movie channels.
Part A: What part of the \$160 charge for the second package is due to the three
movie channels? \$ 30 for three movies.

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Foundations of Mathematical Reasoning Version 3.0 (2020)
Student Pages
Copyright © 2020, The Charles A. Dana Center at The University of Texas at Austin
Part B: What is the per premium movie channel charge?
\$ 30 for three movies. Hence, \$10 for one movie
Part C: What would the total charge be for a package with 9 premium movie
channels?
\$130 + \$90 = \$220
3) Samuel plans to order flowers for his mother, to be delivered on her birthday. A
bouquet of 6 roses will cost \$38, while a larger bouquet of 12 roses will cost \$56.
Part A: If the relationship between the number of roses and the price is linear, what
is the slope (put money in the numerator)? Be sure to include units.
A Rose is = \$3 [ ( 56-38)/6]
Part B: Based on that slope, how much of the price for the smaller bouquet is for
the roses?
\$18 for a small bouquet.
Part C: What is the fixed cost for delivery?
Fixed delivery cost will be \$20
Because for a small bouquet = \$18 + \$20 = \$36
Larger bouquet = \$36 + \$20 = \$56
4) Not all linear relationships describe increasing quantities. For example, if a student
embarks on a weight loss program and averages a loss of 2 pounds per week,
then larger values of “weeks on the diet” are related to lower values of “weight.”
Consider the points:
(8 weeks, 198 pounds) and (11 weeks, 192 pounds)
If we calculate the slope in this relationship using the method developed in class:
slope =
192 pounds - 198 pounds= -2 pounds
11 weeks - 8 weeks 1 week
Based strictly on the slope, 10 weeks on the diet would be associated with a loss
of 194 pounds.
5) Marcus has his car insurance payment directly withdrawn from his savings
account. One month after starting the payment, he had \$915 in savings. Nine
months after starting the payment, he had \$235. Assume Marcus made no other
deposits or withdrawals from the account.

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Foundations of Mathematical Reasoning Version 3.0 (2020) Student Pages Practice Assignment 16.C 1) Two servers at a restaurant start their work shift just as a banquet is being prepared. The number of plates that has been prepared for serving after a certain number of minutes has passed is shown in the table below. 𝑥 = number of minutes that have passed 2 3 8 𝑦 = number of plates prepared 32 38 68 Part A: Look at the first two data points in the table. What do they tell you about the slope of the relationship between the number of minutes that have passed and the number of plates prepared? Write a sentence about this relationship. Be specific and be sure to include units. 6 plates were served within the second and third minute. Part B: Calculate the slope using the second and third data points from the table. What does the slope tell you? Slope is 6. (30/5) Which means 6 plates per minute within 3rd and 8th minutes. Part C: How does your response to Part B compare to Part A? Both slopes are equal. Part D: Calculate the slope for the first and third points. Slope is 36/6 = 6 Which means 6 plates per minute within 2nd and 8th minutes. Part E: Do you have enough inform ...
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