two friends, eliza and margo, go shopping and find a buy-two-pairs-get-one-pair-free sale at a shoe store

Question

two friends, eliza and margo, go shopping and find a buy-two-pairs-get-one-pair-free sale at a shoe store. The least expensive pair is the free one. Eliza finds two pairs she'd like to buy: one for $83.95 and one for $67.95. Margo is interested in a pair that costs $59.95. Eliza and Margo decide to buy the three pairs together, so the pair that costs $59.95 will be free. How should Eliza and Margo divide fairly the total cost of the three pairs of shoes? First, solve this problem on your own, then discuss your solution with the group. Explain your solution method and explain why you think it is a fair way to split the cost of the shoes. Note that different people may have different views of what is "fair".

Answer 1

The three pairs of jeans cost

$83.95

$67.95

$59.95

 

If they had to pay for all three pairs of jeans, the total cost would be $211.85

But they only pay for the two more expensive pairs $151.90

 

Since Eliza purchases the two more expensive pairs of jeans, her share of the total cost should be

151.90           x

--------  = --------

211.85      151.90

 

Cross multiply and solve for x

23073.61 = 211.85x

x = 108.91

 

Then Margo would pay

151.90 - 108.91 = 42.99

 

This way they each received a proportional share of the discount.