Please help. Thanks a lot.

A and C received some money from their mother. C would have $32 more than A if A gave 2/5 of his share to C. C would have $96 more than A if A gave 2/3 of his share to C. How much money did A receive from his mother?
(Non-algebraic method please)

Hearty wrote:
A and C received some money from their mother. C would have $32 more than A if A gave 2/5 of his share to C. C would have $96 more than A if A gave 2/3 of his share to C. How much money did A receive from his mother?
Case 1
A-2A/5+32=C+2A/5
C-A/5=32
5C-A=160

Case 2
A-2A/3+96=C+2A/3
C+A/3=96
3C+A=288

8C=448
C=56
A=120

Amount of money that A received from his mother = $120
Sorry, pls wait for others to post non-algebraic method.

Check
A: $120
C: $56

A gave 2/5 of his share to C-> 2/5x$120=$48
A: $120-$48=$72
C: $56+$48=$104
$104-$72=$32 (Correct)

A gave 2/3 of his share to C-> 2/3x$120=$80
A: $120-$80 = $40
C: $56+$80=$136
$136-$40 = $96 (Correct)

A and C received some money from their mother. C would have $32 more than A if A gave 2/5 of his share to C. C would have $96 more than A if A gave 2/3 of his share to C. How much money did A receive from his mother?

Here is a model drawing approach for this Gap & Difference question

Hi Chris

Good evening

Happen to see this question in my son's fraction revision paper. The answer key show the model like yours but both my son and I cannot understand. This is how he solved the problem as he is not good with model.

get the common denominator for both cases

2/5 -- 6/15 A gave C 6u and left 9u (lst case)
2/3 -- 10/15 A gave C 10u and left 5u (2nd case)

Since this is internal transfer total will not change

1st case total --- 9u + 9u + $32 --- 18u + $32
2nd case total --- 5u + 5u + $96 --- 10u + $96

18u + $32 = 10u + $96
8u --- $64
1u --- $8
A received --- $8 x 15 = $120

Hope this is another road lead to Rome.

Fabulous solution. He has done well to recognize this. I agree that these problem sums produce models that are hard to understand. Furthermore they are a pain to draw too

Do you let me know if you wish further explanation on the model as an alternative approach. Personally, IMO, if he can spot unitary style solutions he will typically be more efficient.

Note: If you compare your units to the model, they are the same

Hi Chris

Thanks for your comments. My son has his way of solving problems and I have come to accept it as long as it is logical. He felt that model drawing is just too difficult for some questions.