SOLUTION: Tom worked for a week from Monday to Friday and was paid $7 per hour. He used 3/5 of his money he earned and an additional $36 to buy some books. He spent 1/2 of the remaining mo

Question 1187547: Tom worked for a week from Monday to Friday and was paid $7 per hour. He
used 3/5 of his money he earned and an additional $36 to buy some books. He
spent 1/2 of the remaining money and an additional $20 on some stationery. He
saved the $32 that was left.
(a) How much did he spend on the stationary?
(b) What was the total number of hours he had worked from Monday to
Friday?
Answer by greenestamps(13208) (Show Source): You can put this solution on YOUR website!

You could set this problem up for solving by starting from the beginning and forming an equation from the given information. It might look something like this....

Let = the total he earned

(1) He spent 3/5 of it, leaving 2/5 of it. The amount remaining was
(2) He then spent $36 more; the amount remaining was
(3) He then spent half the remaining amount, leaving him with the other half. The amount remaining was
(4) He then spent another $20; the amount remaining was

That amount remaining at the end was $32:

That equation looks messy; but in fact solving it is not very difficult. However, if there had been more steps of him spending more money, the equation would have been really ugly.

Usually it is easier to solve a problem like this by working backwards. Here is what it would look like in this problem.

He ended with $32 after spending $20, so he had $32+$20 = $52 before that.
Before that, he spent half his money, so the $52 he had left was half of what he had before. So before that he had 2*($52) = $104.
Before that, he spent $36, so before he spent that he had $104+$36 = $140.
Before that, he spent 3/5 of his money, leaving him with 2/5 of what he had before. So the $140 he had was 2/5 of what he had before. The amount he had before was $140*(5/2) = $350.

He started with $350.

CHECK:
start: $350
spend 3/5 of $350 = $210; left with $140
spend $36; left with $104
spend half of $104 = $52; left with $52
spend $20; left with $32 correct

ANSWERS:
(a) The amount he spent on stationery is given in the statement of the problem: $20

(b) At $7 per hour, the number of hours he worked to earn $350 was 350/7 = 50.

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