PROBLEM SOLVING

[specialnei]

• • 
    Isaiah spent 3/8 on a shirt and 1/5 of the remainder on a wallet. the wallet cost $80.00. how much money did isaiah have remaining

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[lookagain]

Isaiah spent 3/8 on a shirt and 1/5 of the remainder on a wallet. the wallet cost $80.00.

how much money did isaiah have remaining

This problem is not as clear/complete. I wonder if you partially copied it from
somewhere else. I believe the following could be the intended interpretation:

"Isaiah spent 3/8 of his money on a shirt and 1/5 of that remainder on a wallet.
The wallet cost $80.00. How much money did Isaiah have remaining after buying
the shirt and the wallet?"

 

[specialnei]

No this is the question from the paper I found it to be quite unclear as well.

 

[Steven G]

So 1/8 of the entire money is $80
Note that (5/8) of (1/5) is 1/8

 

[The Highlander]

So 1/8 of the entire money is $80
Note that (5/8) of (1/5) is 1/8

Correct, of course, except (from a logic PoV) I would have expressed it as \(\displaystyle \frac{1}{5}\) of \(\displaystyle \frac{5}{8}\) rather than "(5/8) of (1/5)" though, ofc, the answer (due to multiplicative commutativity) is exactly the same, ie: \(\displaystyle \frac{1}{8}\).

The "logic", as I see it, is that having spent \(\displaystyle \frac{3}{8}\) of his money on the shirt, he has \(\displaystyle \frac{5}{8}\) left to spend on the wallet. Since he then spends \(\displaystyle \frac{1}{5}\) of that \(\displaystyle \frac{5}{8}\) he has therefore spent \(\displaystyle \frac{1}{8}\) (\(\displaystyle \frac{1}{5}\) x \(\displaystyle \frac{5}{8}\)) of the initial sum on the wallet purchase and that (\(\displaystyle \frac{1}{8}\)) amounts to $80.