## Friday, January 06, 2012

### Logic at the Mall

I got this one from edhelper.com:

Cody, Benjamin, Sean, Cameron, Aaron, and Jordan each had a different amount of money. They all went to the mall and brought their money. At the mall, each person spent a fraction of the money they started out with. They started out with: \$72, \$24, \$66, \$18, \$48, and \$60. At the mall one spent 1/3 of their money, one spent 1/3 of their money, one spent 5/6 of their money, one spent 1/6 of their money, one spent 2/3 of their money, and one spent 1/2 of their money.

How much money did each person spend at the mall? How much money does each person have left?

1. Benjamin spent more than 1/6 of his money.
2. Cameron spent less than 5/6 of his money.
3. Cody did not spend 1/2 of his money.
4. Jordan spent less than 1/2 of his money.
5. Jordan spent \$24.
6. Sean has \$15 left after spending money at the mall.
7. Cody spent \$33.
8. The person that started out with \$24, has \$8 left after shopping.
9. Cameron has \$40 left after spending money at the mall.
10. Cameron did not spend 2/3 of his money.
11. The person that started out with \$60, has \$40 left after shopping.
12. Benjamin did not spend 1/6 of his money.
13. Aaron did not spend 1/3 of his money.
14. Benjamin has \$8 left after spending money at the mall.

1. Cameron: (9;11) (start 60 spent 1/3 left 40)
Benjamin: (8;14) (start 24 spent 2/3 left 8)
Jordan: (4;5) (start 72 spent 1/3 = 24)

(Jordan could either spend 1/3 or 1/6 (only options less then 1/2) wherease 1/6 would give a start 144, no option!)

Cody (3;7) here it doesn't add up
only spent options left: 1/6 or 5/6
he spent 33
which gives, start 198 or 39.6 respectively. Not options!

2. I went with there being a typo on Cody.

Aaron 5/6 \$48
Benjamin 2/3 \$24
Cameron 1/3 \$60
Cody 1/2 \$66
Jordan 1/3 \$72
Sean 1/6 \$18

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