SOLUTION: Hi Haresh gave 1/6 of his money to Jane. He spent $8 less than 1/3 of the remaining money on books. Haresh had $68 left. How much did he have at first. My son solved it by worki

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Question 1206129: Hi
Haresh gave 1/6 of his money to Jane. He spent $8 less than 1/3 of the remaining money on books. Haresh had $68 left. How much did he have at first.
My son solved it by working backwards, can you show how to solve it algebraically.


Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13196) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the number of dollars he had to start.

After he gave 1/6 of it to Jane, the number he had left was %285%2F6%29x.

1/3 of what he had left was %281%2F3%29%2A%285%2F6%29x=%285%2F18%29x

$8 less than what he had left was %285%2F18%29x-8

After spending that amount, the amount he had left was %285%2F6%29x-%28%285%2F18%29x-8%29=%2810%2F18%29x%2B8=%285%2F9%29x%2B8

The amount he had left was $68:

%285%2F9%29x%2B8=68
%285%2F9%29x=60
x=60%289%2F5%29=9%2A12=108

ANSWER: $108

CHECK:
start: $108
give away 1/6 = $18; $90 left
spent $8 less than 1/3 of what he had left = (1/3)$90-$8 = $30-$8 = $22
amount he finished with: $90-$22 = $68

Answer by ikleyn(52764) About Me  (Show Source):
You can put this solution on YOUR website!
.
Haresh gave 1/6 of his money to Jane. He spent $8 less than 1/3 of the remaining money on books.
Haresh had $68 left. How much did he have at first.
My son solved it by working backwards, can you show how to solve it algebraically.
~~~~~~~~~~~~~~~~~~~~~ 

Let x be the amount Haresh had at first.

After Haresh gave 1/6 of his money to Jane, his remaining amount is 5x%2F6.


He spent on books %281%2F3%29%2A%28%285x%29%2F6%29%29-8 = %285x%2F18%29-8.


After that, his remaining money is %285x%29%2F6 - %28%285x%29%2F18+-8%29 = %2810x%29%2F18+%2B+8.


This amount is 68 dollars.  So, the equation is

    %2810x%29%2F18+%2B+8 = 68.


To solve, multiply all the terms by 18

   10x + 8*18 = 18*68

   10x       = 18*68-8*18

   10x       = 1080

     x       = 1080/10 = 108.


ANSWER.  Haresh had $108 at first.

Solved.