Question 1207197
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Let x be the amount Ben paid.
Then x+10 is the amount Cathy paid.<br>
The amount Alisha paid was 3/5 of the total that Ben and Cathy paid:
{{{(3/5)(x+x+10) = (6/5)x+6}}}<br>
So the total amount spent was
{{{x + x+10 + (6/5)x+6 = (16/5)x+16}}}<br>
Daniel repaid $24 to Alisha, so Alisha's equal share was {{{(6/5)x+6 - 24 = (6/5)x-18}}}<br>
Since Alsiha's share was {{{(16/5)x-18}}}, the total spent was
{{{4((6/5)x-18) = (24/5)x-72}}}.<br>
The two expressions for the total amount spent must be equal:<br>
{{{(16/5)x+16=(24/5)x-72}}}
{{{88=(8/5)x}}}
{{{x=55}}}<br>
Results so far....
Ben spent x = $55
Cathy spent x+10 = $65
Alisha spent (6/5)x+6 = $66+$6 = $72
The total amount spent was $55+$65+$72 = $192<br>
The equal shares were $192/4 = $48<br>
Daniel repaid $24 to Alisha, making Alisha's share correct: $72-$24 = $48<br>
Since the equal shares were $48 each, and since Daniel repaid $24 to Alisha, the amount he repaid to Ben and Cathy was $48-$24 = $24.<br>
ANSWER: Daniel repaid $24 to Ben and Cathy<br>
It's not clear from the wording of the question whether we need to know how much Ben got from Daniel and how much Cathy got.  If that was the intent of the question, then we only need to divide the $24 Daniel repaid to Ben and Cathy into two parts with Cathy's part being $10 more than Ben's.  That leads to<br>
ALTERNATIVE ANSWER: Daniel repaid $17 to Cathy and $7 to Ben<br>