given equations that represent the proportional relationship between the total cost, t and the...
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![Page 1: Given equations that represent the proportional relationship between the total cost, t and the number of items, n, how do you determine the best deal?](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649f275503460f94c3f166/html5/thumbnails/1.jpg)
Given equations that represent the proportional relationship between the total cost, t and the
number of items, n, how do you determine the best deal?
For example: Which candy is the best deal?
Candy Equation
A t = 0.1 n
B t = 0.02 n
C t = 0.03 n
![Page 2: Given equations that represent the proportional relationship between the total cost, t and the number of items, n, how do you determine the best deal?](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649f275503460f94c3f166/html5/thumbnails/2.jpg)
In this lesson you will learn how to determine the best deal
by comparing equations that represent the proportional
relationship between the total cost, t and the number of
items, n.
![Page 3: Given equations that represent the proportional relationship between the total cost, t and the number of items, n, how do you determine the best deal?](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649f275503460f94c3f166/html5/thumbnails/3.jpg)
Let’s Review
Unit Cost
Total Cost
Total Items
= Cost
One Item
$150
2 bikes
= $75
1 bike
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Let’s Review
Writing Equation
dependent variable = t = total costindependent variable = n = number of items
constant of proportionality = unit costunit cost = t n
t = unit cost x n
![Page 5: Given equations that represent the proportional relationship between the total cost, t and the number of items, n, how do you determine the best deal?](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649f275503460f94c3f166/html5/thumbnails/5.jpg)
A Common Mistake
Forgetting about the place value when
comparing decimals
0.2
0.03
>
0.04
0.3
<
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Core Lesson
Which candy is the best deal?
Candy Equation
A t = 0.1 n
B t = 0.02 n
C t = 0.03 n
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Core Lesson
Total Cost = Unit Cost x Number of Items
t = Unit Cost x n
Lowest unit cost is the best deal t = 0.1 n t = 0.02 nt = 0.03 n
![Page 8: Given equations that represent the proportional relationship between the total cost, t and the number of items, n, how do you determine the best deal?](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649f275503460f94c3f166/html5/thumbnails/8.jpg)
Core Lesson
Candy A = 0.1Candy B = 0.02Candy C = 0.03
0.1 > 0.03 > 0.02
Candy B is the best deal
Unit Price
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Core Lesson
Items Candy A Cost
Candy B Cost
Candy CCost
0 0 0 0
1 0.10 0.02 0.03
2 0.20 0.04 0.06
3 0.30 0.06 0.09
4 0.40 0.08 0.12
Table of Cost per Item
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Core Lesson
Graph of Cost per Item
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
0.050.1
0.150.2
0.250.3
0.350.4
0.45
Candy A Cost Candy B Cost Candy C Cost
Items
Cost
![Page 11: Given equations that represent the proportional relationship between the total cost, t and the number of items, n, how do you determine the best deal?](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649f275503460f94c3f166/html5/thumbnails/11.jpg)
In this lesson, you have learned how to determine the
best deal by comparing equations that represent the
proportional relationship between the total cost, t, and
the number of items, n.
![Page 12: Given equations that represent the proportional relationship between the total cost, t and the number of items, n, how do you determine the best deal?](https://reader036.vdocuments.net/reader036/viewer/2022062422/56649f275503460f94c3f166/html5/thumbnails/12.jpg)
Guided Practice
Which candy is the best deal?
Candy Equation
A t = 0.08n
B t = 0.2n
C t = 0.05n
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Extension Activities
Given the information in the table, find the unit cost for each soda offer. Then for each offer write an equation that relates the total cost, t to the number of units, n. Finally, determine which offer is the best deal and explain your reasoning.
Amount Cost
32 ounce $ 0.99
Six 12 ounce bottles $ 4.99
Twelve 8 ounce cans $ 2.99
2 liters $ 1.29
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Extension Activities
Write a letter to a friend that explains how to find the best deal. Be sure to discuss if the number of items determines which item is the best deal and provide examples of when the best deal is in the lower number of items and when it is in the greater number of items. Also, address whether the best deal is always the best choice? Think of at least two situations when it may not be the best choice.
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Quick Quiz
1) Which pencil brand is a better deal?t = 0.09 nt = 0.4 n
2) Which cereal brand is a better deal?t = 0.07 nt = 0.3 n