SOLUTION: Benjamin had a sum of money. He spent $288 on a watch and 3/8 of the remainder of a belt. He had 2/5 of his money left in the end. What fraction of the money did he spend on th

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Benjamin had a sum of money. He spent $288 on a watch and 3/8 of the remainder of a belt. He had 2/5 of his money left in the end. What fraction of the money did he spend on th      Log On


   

Question 1119763: Benjamin had a sum of money. He spent $288 on a watch and 3/8 of the remainder of a belt. He had 2/5 of his money left in the end.
What fraction of the money did he spend on the watch?
How much money did he have at first?

I have no idea how to tackle this question. Can someone advise how I would calculate?
Thanks in advance.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
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Benjamin had a sum of money. He spent $288 on a watch and 3/8 of the remainder of a belt. He had 2/5 of his money left in the end.
What fraction of the money did he spend on the watch?
How much money did he have at first?
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x, the original sum of money

Spent $288, and 3%2F8 of what was present after spending the $288.
He then had %28x-288%29%2B%285%2F8%29%28x-288%29 dollars, after the two purchases.


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He had 2/5 of his money left in the end.
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highlight_green%28%28x-288%29%2B%285%2F8%29%28x-288%29=%282%2F5%29x%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Benjamin had a sum of money. He spent $288 on a watch and 3/8 of the remainder of a belt. He had 2/5 of his money left in the end.
What fraction of the money did he spend on the watch?
How much money did he have at first?

I have no idea how to tackle this question. Can someone advise how I would calculate?
Thanks in advance.
Correct answer: highlight_green%28%22%24800%22%29. 

Any other answer deserves to be thrown in the GARBAGE, which includes an equation by a person who responded to your math problem.

Let me show it to you: cross%28highlight_green%28%28x-288%29%2B%283%2F8%29%28x-288%29=%282%2F5%29x%29%29 <====== GARBAGE



Let the original amount be A

Then after spending $288, he had A - 288 remaining

After spending 3%2F8 of the remaining (A - 288), he had 

Now, since in the end he had 2%2F5 of the original amount remaining, we can say that: 

matrix%281%2C3%2C+5%28A+-+288%29%2F8%2C+%22=%22%2C+2A%2F5%29

16A = 5(5)(A - 288) -------- Cross-multiplying

16A = 25A - 25(288)

16A - 25A = - 25(288)

- 9A = - 25(288)

A, or amount he initially had was: