John spent 3/5 of his money on books and 1/3 of the remainder on a wallet.
If John had $16 left, how much did he have at first?
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Let's solve this step by step. John spent three-fifths of his money on books and one-third of the remainder on a wallet. He had sixteen dollars left. We need to find his original amount.
First, let's find what fraction of money John has left after buying books. He spent three-fifths on books, so the remainder is one minus three-fifths, which equals two-fifths of his original amount.
Next, John spent one-third of the remainder on a wallet. Since the remainder was two-fifths of his original amount, the money left after buying the wallet is two-thirds of the remainder. This equals two-thirds times two-fifths, which is four-fifteenths of his original amount.
Now we can set up an equation. We know that four-fifteenths of the original amount equals sixteen dollars. To find the original amount, we need to solve this equation by dividing sixteen by four-fifteenths, which is the same as multiplying sixteen by fifteen-fourths.
Finally, let's calculate the answer. Sixteen times fifteen-fourths equals sixteen times fifteen divided by four, which is two hundred forty divided by four, equals sixty dollars. We can verify: John spent thirty-six dollars on books, had twenty-four dollars remaining, spent eight dollars on a wallet, leaving sixteen dollars. Therefore, John originally had sixty dollars.