SOLUTION: Frank bought supplies for school. In the first store, he spent half of his money plus $10. In the second store, he spent half of what he had left, plus $10. In the third store,

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Question 1090357: Frank bought supplies for school. In the first store, he spent half of his money plus $10. In the second store, he spent half of what he had left, plus $10. In the third store, he spent 80% of what he had left. He came home with $5. How much did he start out with?
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Frank bought supplies for school. In the first store, he spent half of his money plus $10.
In the second store, he spent half of what he had left, plus $10.
In the third store, he spent 80% of what he had left.
He came home with $5. How much did he start out with?
:
let x = initial amt
"In the first store, he spent half of his money plus $10."
x - (.5x + 10) = .5x - 10, amt left after first store
:
"In the second store, he spent half of what he had left, plus $10."
(.5x-10) - (.5(.5x-10) + 10)
.5x - 10 - (.25x + 5 + 10)
.5x - 10 - .25x - 5 - 10 = .25x - 15 amt left after the 2nd store
:
In the third store, he spent 80% of what he had left. He came home with $5.
(.25x - 15) - (.8(.25x-15) = 5
.25x - 15 - (.2x - 12) = 5
.25x - 15 - .2x + 12 = 5
.05x - 3 = 5
.05x = 5 + 3
x = 8/.05
x = 160 is the initial amt
:
How much did he start out with? $160
:
;
Check this out
1. 160 - (80+10) = $70
2. 70 - (35+10) = $25
3. 25 - .8(25) = 25 - 20 = 5