If Diana gives David $23, the amount of money she has will be 30% of his. If David gives Diana $54, he will have the same amount of money as her. How much money did each of them have?
(a) David
(b) Diana

	Case 1		Case 2
	David	Diana	David	Diana
Before	10 u - 23	3 u + 23	6.5 u + 54	6.5 u - 54
Change	+ 23	- 23	- 54	+ 54
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

In Case 1, when Diana gives to David, there is an internal transfer of money from Diana to David.  The total amount that both have remains the same.

In Case 2, when David gives to Diana, there is an internal transfer of money from David to Diana. The total amount that both have remains the same.

The total amount that both have in Case 1 and Case 2 are the same.

Total amount that Diana and David have
= 10 u + 3 u
= 13 u

Amount that Diana and David each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u

Amount that David has at first is the same in Case 1 and Case 2.

10 u - 23 = 6.5 u + 54
10 u - 6.5 u = 54 + 23
3.5 u = 77 

1 u = 77 ÷ 3.5 = 22

Amount that David has
= 10 u - 23
= 10 x 22 - 23
= 220 - 23
= $197 

(b)
Amount that Diana has
= 3 u + 23
= 3 x 22 + 23
= 66 + 23
= $89

Answer(s): (a) $197; (b) $89