The Shoe Sale

This problem is from Peter Liljedahl's site.

The Shoe Sale

You decide to take advantage of a buy 2 pair get 1 pair of equal or lesser value for free sale at the local shoe store. The problem is that you only want to get two pairs of shoes. So, you bring your best friend with you to the store. After much deliberation you settle on two pairs of shoes – a sporty red pair for $20 and a dressy black pair for $55. You friend finds a practical cross trainer for $35. When you proceed to the check out desk the cashier tells you that your bill is $90 plus tax (the $20 pair are for free). How much should each of you pay? Justify your decision.

Peter lists this problem under "Senior High School (10-12)." I give it to both my 6th and 8th graders. I like this problem because I like hearing how kids think about "fair sharing." A few 6th graders think each person should pay $45. I don't think these kids have too many friends. (That was mean.)

One of my 6th graders says one person should pay 2/3 of the $90 and the friend pays 1/3. But her answers are $59.40 and $29.60, respectively. My math says 2/3 of 90 is 60, so I call her up to explain. She has her calculator in hand, and I see her punch in .66 while mouthing "two thirds."

It was an opportunity for me to yell and scream at the children for turning a perfectly good number of 2/3 into mush.