document.write( "Question 1208419: Hi
\n" ); document.write( "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.
\n" ); document.write( "What was the sum of money shared by the three of them. \n" ); document.write( "
Algebra.Com's Answer #847047 by MathTherapy(10552)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Hi\r\n" );
document.write( "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. \r\n" );
document.write( "What was the sum of money shared by the three of them.\r\n" );
document.write( "\r\n" );
document.write( "Ratio of Mrs. Johnson's share to Bernard's: 5:2\r\n" );
document.write( "Ratio of Bernard's share to Raymond's: 3:4\r\n" );
document.write( "Bernard's part 2, in the ratio, 5:2 needs to MATCH with his part 3, in the ratio 3:4\r\n" );
document.write( "To do this, we need to MULTIPLY the 1st ratio by 3, and the 2nd by 2\r\n" );
document.write( "The 1st ratio, 5:2 becomes: 3(5):3(2) = 15:6\r\n" );
document.write( "The 2nd ratio, 3:4 becomes: 2(3):2(4) = 6:8\r\n" );
document.write( "We now get the following 3-part ratio for Mrs. Johnson, Bernard, and Raymond: 15:6:8\r\n" );
document.write( "\r\n" );
document.write( "Let the multiplicative FACTOR be x\r\n" );
document.write( "Then Mrs. Johnson, Bernard, and Raymond get: 15x, 6x, and 8x, respectively, for a total of 29x (15x + 6x + 8x)\r\n" );
document.write( "After receiving 20% (\"1%2F5\") of Mrs. Johnson's share, or \"matrix%281%2C5%2C+1%2F5%2C+of%2C+15x%2C+%22=%22%2C+3x%29\", Raymond then had 8x + 3x = 11x\r\n" );
document.write( "After donating (\"1%2F3\") of his share to charity, or \"matrix%281%2C5%2C+1%2F3%2C+of%2C+6x%2C+%22=%22%2C+2x%29\", Bernard ended up with 6x - 2x = 4x\r\n" );
document.write( "As Raymond had $4,270 more than Bernard in the end, we get: 11x - 4x = 4,270\r\n" );
document.write( "                                                                  7x = 4,270\r\n" );
document.write( "                                        Multiplicative factor, or \"matrix%281%2C5%2C+x%2C+%22=%22%2C+%224%2C270%22%2F7%2C+%22=%22%2C+%22%24610%22%29\"\r\n" );
document.write( "\r\n" );
document.write( "Subsituting MULTIPLICATIVE FACTOR, 610 for x, AMOUNT SHARED by the 3 = 29(x) = 29($610) = $17,690
\n" ); document.write( "
\n" );