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?

Algebra ->  Percentage-and-ratio-word-problems -> 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?      Log On


   

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) About Me  (Show Source):
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To follow the description's steps exactly, x for the money at start, then equation is x-360-%28x-360%29%2F7=2x%2F5. That is, if you wish to solve the problem's question this way.


x=675

Answer by ikleyn(52788) About Me  (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 - %281%2F7%29%2A%28x-360%29 = %282%2F5%29x.


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) About Me  (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:

%286%2F7%29y=%282%2F5%29x
y=%287%2F6%29%282%2F5%29x=%287%2F15%29x

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:

360=%288%2F15%29x
x=%2815%2F8%29%28360%29=15%2845%29=675

ANSWER: $675

Answer by MathTherapy(10552) About Me  (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 1%2F7 of remainder, he had 
Also, it's given that he had 2%2F5 of his money left. This would be: matrix%281%2C3%2C+%282%2F5%29A%2C+or%2C+2A%2F5%29
We now equate the 2 remainders to get: matrix%281%2C3%2C+%286A+-+%222%2C160%22%29%2F7%2C+%22=%22%2C+2A%2F5%29
                                              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