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

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.

Let’s Review

Unit Cost

Total Cost

Total Items

= Cost

One Item

$150

2 bikes

= $75

1 bike

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

A Common Mistake

Forgetting about the place value when

comparing decimals

0.2

0.03

>

0.04

0.3

<

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

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

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

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

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

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.

Guided Practice

Which candy is the best deal?

Candy Equation

A t = 0.08n

B t = 0.2n

C t = 0.05n

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

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.

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