The Shoe Sale

(On a side note, I’m not sure what I love more, my left foot or Google Classroom.)

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.

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  1. Posted May 1, 2016 at 9:07 am | Permalink

    This is a brilliant problem. Anybody, eventually, can do the sums, but which sum to do is scarily “real world”.
    I trust there would have been a bit less screaming if she had put 0.67 in instead!

  2. Chris
    Posted May 1, 2016 at 11:31 am | Permalink

    You find the coolest problems. How do you find these sites in the first place? Like the Good Burger problem from a while back. Awesome.

  3. Posted June 22, 2016 at 9:50 am | Permalink

    Great information. Lucky me I found your website by accident (stumbleupon).
    I’ve saved it for later!

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