Question 1206129
.
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.
~~~~~~~~~~~~~~~~~~~~~


<pre>
Let x be the amount Haresh had at first.

After Haresh gave 1/6 of his money to Jane, his remaining amount is {{{5x/6}}}.


He spent on books {{{(1/3)*((5x)/6))-8}}} = {{{(5x/18)-8}}}.


After that, his remaining money is {{{(5x)/6}}} - {{{((5x)/18 -8)}}} = {{{(10x)/18 + 8}}}.


This amount is 68 dollars.  So, the equation is

    {{{(10x)/18 + 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.


<U>ANSWER</U>.  Haresh had $108 at first.
</pre>

Solved.