Question 345086: John took all his money out his savings account. He spent $50 on a radio and 3/5 of what remained on presents. Half of what was left he put back in his checking account, and the remaining $35 he donated to charity. How much money did John originally have in his savings account?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! This is a fun question. it just takes several steps.
Start by picking a variable to represent "all his money in his savings account." Let's call that 'x'.
He spent 50 on a radio.
He spent 3/5 of what was left on presents.
"What was left" was x-50, so we define this as
3/5*(x-50) = what he spent on presents.
He put half of "what was left" back into the checking account.
"And the remaining 35 he donated to charity."
Hmm. That means "half of what was left" = 35.
Looking back, the nearest definition of "what was left" is 2/5(x-50), since he spent 3/5(x-50) on presents.
1/2 of 2/5 = 1/5.
So,
1/5(x-50) = 35
Multiply both sides by 5 to get rid of the fraction.
x-50 = 175
Add 50 to both sides.
x = 225
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Now check the work.
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225 - 50 = 175, after buying the radio.
3/5(175) = 105, which is the 3/5 he spent on presents.
175 - 105 = 70, which he split in half: 35 for charity and 35 into checking.
That matches the setup, so we're almost done.
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What was the question? "How much money did John originally have in his savings account?"
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John had $225 in his savings account originally.
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Done.
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