If Dana gives Carl $22, the amount of money she has will be 30% of his. If Carl gives Dana $76, he will have the same amount of money as her. How much money did each of them have?
(a) Carl
(b) Dana

	Case 1		Case 2
	Carl	Dana	Carl	Dana
Before	10 u - 22	3 u + 22	6.5 u + 76	6.5 u - 76
Change	+ 22	- 22	- 76	+ 76
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

In Case 2, when Carl gives to Dana, there is an internal transfer of money from Carl to Dana. 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 Dana and Carl have
= 10 u + 3 u
= 13 u

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

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

10 u - 22 = 6.5 u + 76
10 u - 6.5 u = 76 + 22
3.5 u = 98 

1 u = 98 ÷ 3.5 = 28

Amount that Carl has
= 10 u - 22
= 10 x 28 - 22
= 280 - 22
= $258 

(b)
Amount that Dana has
= 3 u + 22
= 3 x 28 + 22
= 84 + 22
= $106

Answer(s): (a) $258; (b) $106