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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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