Question 1208419
<pre>
Hi
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.

Ratio of Mrs. Johnson's share to Bernard's: 5:2
Ratio of Bernard's share to Raymond's: 3:4
Bernard's part 2, in the ratio, 5:2 needs to MATCH with his part 3, in the ratio 3:4
To do this, we need to MULTIPLY the 1<sup>st</sup> ratio by 3, and the 2<sup>nd</sup> by 2
The 1<sup>st</sup> ratio, 5:2 becomes: 3(5):3(2) = 15:6
The 2<sup>nd</sup> ratio, 3:4 becomes: 2(3):2(4) = 6:8
We now get the following 3-part ratio for Mrs. Johnson, Bernard, and Raymond: 15:6:8

Let the multiplicative FACTOR be x
Then Mrs. Johnson, Bernard, and Raymond get: 15x, 6x, and 8x, respectively, for a total of 29x (15x + 6x + 8x)
After receiving 20% ({{{1/5}}}) of Mrs. Johnson's share, or {{{matrix(1,5, 1/5, of, 15x, "=", 3x)}}}, Raymond then had 8x + 3x = 11x
After donating ({{{1/3}}}) of his share to charity, or {{{matrix(1,5, 1/3, of, 6x, "=", 2x)}}}, Bernard ended up with 6x - 2x = 4x
As Raymond had $4,270 more than Bernard in the end, we get: 11x - 4x = 4,270
                                                                  7x = 4,270
                                        Multiplicative factor, or {{{matrix(1,5, x, "=", "4,270"/7, "=", "$610")}}}

Subsituting MULTIPLICATIVE FACTOR, 610 for x, <font color = red><font size = 4><b>AMOUNT SHARED by the 3</font></font></b> = 29(x) = 29($610) = <font color = red><font size = 4><b>$17,690</font></font></b></pre>