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James gave 1/4 of his money to his mother. He spent 5/18 of the remainder on a wallet and 2 CDs and had $78 left. The wallet cost 4 times as much as a CD.
(a) How much money did James have at first?
(b) What was the cost of one CD?

This means that $78 is 1 - 5/18 = 13/18 of what he had after he gave 1/4 to his mother.
Since $78 is 13/18, multiply both by 18/13 to get that amount.
Now 1/13 of 78 is 6, and 6 times 18 is 108, so that means before the wallet and CDs he had $108.

To find out how much he had before he gave 1/4 to his mother, we need to know he 3/4 of his starting amount.  This 3/4 of his starting amount is 108, so multiplying by 4/3 gives us
4*36 = 144.  This means he started with $144.

Going back to check, he gave a four the his mom, and 1/4 of 144 is 36, and 144 - 36 = 108.
It says the wallet and 2 CDs cost 5/18 of this amount.  Since 1/18 is $6, 5/18 is $30.
This leaves him with $108 - $30 = $78, and that's what we were told.

Let the price of a CD be x.  Now if the wallet was four times as much as a CD, and there were 2CD's, that means we had 4x + x + x = 78, or 6x = 78.  Dividing both sides by 6 gives x = 13.

Looking back at the answer I just gave, the answer to (a) was the amount at the start and
the answer to (b) was the cost of a CD.  Both of those have been stated already.  All that's left to do is look back and see what they were.

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Scott A Wilson


I have answered every question that was a story problems that had any relation to math for which an answer existed. I have ever answered some questions which had a vague relation to math, but still related.


My experience is from when I started doing story problems in grade school. I have been assisting, helping, and bringing smiles to many others ever since. Are you the next one?

In over 850 questions answered to other users. Maybe you're the next one ...

I received a BA in Mathematical Sciences from OSU and a MS in Mathematics from OSU as well.

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I earned Both my BS degree and MS degree with honors for having such a high grade point average.

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I have answered hundreds and hundreds of students at OSU in the 80's and over 8,500 questions right here, but only a little over 850 of them have been word problems.

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