SOLUTION: After spending 3/8 of on food and 1/4 on housing, sonny was left with $960. How much money did he have originally

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Question 767056: After spending 3/8 of on food and 1/4 on housing, sonny was left with $960. How much money did he have originally
Found 2 solutions by josgarithmetic, nerdybill:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Original money quantity, N.
N-%283%2F8%29N-%281%2F4%29N=960 fits the description of spending portions from N and having 960 as a result after that spending occurred.

From that equation, you can factor N on the left side, and you have a couple of choices how to go next.

N%281-3%2F8-1%2F4%29=960
Maybe just do the arithmetic computation in denominations of (1/8) units.
1-3%2F8-1%2F4=8%2F8-3%2F8-2%2F8
%288-3-2%29%2F8=%288-5%29%2F8=3%2F8

That allows revising equation to:
N%283%2F8%29=960
N=960%288%2F3%29
N=%28960%2F3%29%2A8=320%2A8
highlight%28N=2560%29

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
After spending 3/8 of on food and 1/4 on housing, sonny was left with $960. How much money did he have originally
.
Let x = amount ($) started with
then
x - (3/8)x - (1/4)x = 960
x(1 - 3/8 - 1/4) = 960
x(8/8 - 3/8 - 2/8) = 960
x((8-3-2)/8) = 960
x(3/8) = 960
x = 960(8/3)
x = 320(8)
x = $2560