# Math

The Mall: My sister likes to go shopping. Yesterday she borrowed a wad of money from Mom and went to the mall. She began her excursion by spending \$18 on a new CD. Then she spent half her remaining money on a new dress. Then she spent \$11 on lunch. Then she spent one-third of her remaining money on a book. On her way home she bought gas for \$12 and spent one-fourth of the remaining money on a discounted CD at the convience store. Finally, she slipped me \$2 when she got home, and gave mom \$10 in change. Mom was furious and demanded an explanation of where the money went. List the items she bought and the amount spent on each item and tell how much she started with."

I think the answer is \$124 but i'm not sure...

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start: \$x
CD: 18, leaving x-18
dress: half that, leaving x/2 - 9
lunch:11, leaving x/2 - 20
book: 1/3 of that, leaving (2/3)(x/2-20) = x/3 - 40/3
gas: 12, leaving x/3 - 76/3
CD: 1/4 of that, leaving (3/4)(x/3 - 76/3) = x/4 - 19
slipped 2, leaving x/4 - 21

so, x/4 - 21 = 10
x = 124

Good work.

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after CD's : x-18
spend 1/2 of that, leaving (x-18)/2
after lunch, amount left = (x-18)/2 - 11
spends 1/3 of that on book leaving with
(2/3)( (x-18)/2 - 11), let's simplify that a bit
= (2/3)(x/2 - 9 - 11)
= (2/3)(x/2 - 20)
= x/3 - 40/3

spent 12 on gas, leaving her with x/3 - 40/3 - 12
= x/3 - 76/3
spent 1/4 of that on another CD
leaving her with (3/4)(x/3 - 76/3)
= x/4 - 19
gave another \$2 away leaving her with \$10
x/4 - 21 = 10
x/4 = 31
x = 124 , yeah you were right.

check:
spend half of that on dress, leaving 53
after lunch , left with 42
1/3 of that on book , leaving (2/3)of 42 or 28
bought gas of \$12, leaving \$16
spent 1/4 of 16 on another CD, leaving 12
after slipping you \$2, amount left is \$10.

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