document.write( "Question 1207222: Aloysius had some money at first. He spent $360 on a suit. He then spent 1/7 of his remaining money on shoes and had 2/5 of his money left. How much money did he have at first? \n" ); document.write( "

Algebra.Com's Answer #844972 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "You have received two responses showing a standard algebraic solution that starts with a direct translation of the given information.

\n" ); document.write( "Here is a solution that starts from an unusual and very different point and makes solving the problem much less work.

\n" ); document.write( "Let x be the amount of money he starts with
\n" ); document.write( "Let y be the amount he has after spending $360 on the suit

\n" ); document.write( "The amount he had left after buying the suit was y. After he bought the suit, he spent 1/7 of that money on shoes, so the amount he had left after buying the shoes was (6/7)y.

\n" ); document.write( "But the amount he had left after buying the shoes was 2/5 of the original amount:

\n" ); document.write( " $\"%286%2F7%29y=%282%2F5%29x\"$
\n" ); document.write( " $\"y=%287%2F6%29%282%2F5%29x=%287%2F15%29x\"$

\n" ); document.write( "Since the amount he had left after buying the suit was 7/15 of the original amount, the cost of the suit was 8/15 of the original amount:

\n" ); document.write( " $\"360=%288%2F15%29x\"$
\n" ); document.write( " $\"x=%2815%2F8%29%28360%29=15%2845%29=675\"$

\n" ); document.write( "ANSWER: $675

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