Question 1208419
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Mrs Johnson and her 2 sons Bernard and raymond shared a sum of money. 
The ratio received by Mrs Johnson to that received by Bernard was 5 to 2 . 
The ratio of money received by Bernard to that received by Raymond was 3 to 4. 
After Mrs Johnson gave 20% of her share to Raymond and Bernard donated 1/3 of his share to charity. 
Raymond then had $4270 more than Bernard.
What was the sum of money shared by the three of them.
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From this statement, "The ratio received by Mrs Johnson to that received by Bernard was 5 to 2",
I choose to write 5x for Mrs. Johnson amount and 2x for the Bernard amount.

Here "x" is the common measure of these amounts, in dollars. 


From the second statement, "The ratio of money received by Bernard to that received by Raymond was 3 to 4"
we conclude that Raymond then received  {{{(4/3)*(2x)}}} = {{{(8x)/3}}} dollars. 


After re-distribution and donation, Raymond has  {{{(8x)/3 + (1/5)*(5x)}}} = {{{(8x)/3 + x}}} = {{{(11x)/3}}} dollars;

                                    Bernard has  {{{2x - (1/3)*(2x)}}} = {{{(2/3)*(2x)}}} = {{{(4x)/3}}}.


Now Raymond has $4270 more than Bernard

    {{{(11x)/3}}} - {{{(4x)/3}}} = 4270  dollars.


The setup is complete. Now we should solve this equation and find x.

Multiply both sides by 3

    11x - 4x = 3*4270

        7x   =  12810

         x   =  12810/7 = 1830.


Thus the sum of money shared by the three of them was  5x + 2x + {{{(8x)/3}}} = {{{5*1830 + 2*1830 + (8*1830)/3}}} = 17690 dollars.


<U>ANSWER</U>.  The sum of money shared by the three of them was  17690 dollars.
</pre>

Solved completely, using only one single unknown variable,

and in a way as it should be done and as it is expected to be done.