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? For example: Which candy is the best deal? CandyEquation At = 0.1 n Bt = 0.02 n Ct = 0.03 n

2. 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.

3. Let’s Review Unit Cost Total Cost Total Items =Cost One Item $150 2 bikes =$75 1 bike

4. Writing Equation dependent variable = t = total cost independent variable = n = number of items constant of proportionality = unit cost unit cost = t n t = unit cost x n

5. A Common Mistake Forgetting about the place value when comparing decimals 0.20.03> 0.040.3<

6. Core Lesson Which candy is the best deal? CandyEquation At = 0.1 n Bt = 0.02 n Ct = 0.03 n

7. 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 n t = 0.03 n

8. Candy A = 0.1 Candy B = 0.02 Candy C = 0.03 0.1 > 0.03 > 0.02 Candy B is the best deal Unit Price

9. ItemsCandy A Cost Candy B Cost Candy C Cost 0000 10.100.020.03 20.200.040.06 30.300.060.09 40.400.080.12 Table of Cost per Item

10. Core Lesson Graph of Cost per Item

11. 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.

12. Guided Practice Which candy is the best deal? CandyEquation At = 0.08n Bt = 0.2n Ct = 0.05n

13. 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. AmountCost 32 ounce$ 0.99 Six 12 ounce bottles$ 4.99 Twelve 8 ounce cans$ 2.99 2 liters $ 1.29

14. 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.

15. Quick Quiz  Which pencil brand is a better deal? t = 0.09 n t = 0.4 n 2) Which cereal brand is a better deal? t = 0.07 n t = 0.3 n