SOLUTION: 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?

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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?
Found 4 solutions by josgarithmetic, ikleyn, greenestamps, MathTherapy:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
To follow the description's steps exactly, x for the money at start, then equation is . That is, if you wish to solve the problem's question this way.




Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
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?
~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Write equation as you read the problem

    x-360 -  = .


To solve it, multiply both sides by 7*5 = 35; then simplify.

    35*(x-360) - 5*(x-360) = 2*7*x,

    30(x-360) = 14x

    30x - 10800 = 14x

    30x - 14x = 10800

        16x   = 10800

          x = 10800/16 = 675.


ANSWER.  Originally, Aloysius had 675 dollars.

Solved.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


You have received two responses showing a standard algebraic solution that starts with a direct translation of the given information.

Here is a solution that starts from an unusual and very different point and makes solving the problem much less work.

Let x be the amount of money he starts with
Let y be the amount he has after spending $360 on the suit

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.

But the amount he had left after buying the shoes was 2/5 of the original amount:




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:




ANSWER: $675
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
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?

Let original amount he had, be A
After spending $360, he had A - 360 left
After spending  of remainder, he had 
Also, it's given that he had  of his money left. This would be: 
We now equate the 2 remainders to get: 
                                              7(2A) = 5(6A - 2,160) ---- Cross-multiplying
                                                14A = 30A - 5(2,160)
                                          14A - 30A = - 5(2,160)
                                              - 16A = - 5(2,160)
                             Original amount, or

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