If Dana gives Fred $16, the amount of money she has will be 30% of his. If Fred gives Dana $61, he will have the same amount of money as her. How much money did each of them have?
(a) Fred
(b) Dana

	Case 1		Case 2
	Fred	Dana	Fred	Dana
Before	10 u - 16	3 u + 16	6.5 u + 61	6.5 u - 61
Change	+ 16	- 16	- 61	+ 61
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

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

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

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

10 u - 16 = 6.5 u + 61
10 u - 6.5 u = 61 + 16
3.5 u = 77 

1 u = 77 ÷ 3.5 = 22

Amount that Fred has
= 10 u - 16
= 10 x 22 - 16
= 220 - 16
= $204 

(b)
Amount that Dana has
= 3 u + 16
= 3 x 22 + 16
= 66 + 16
= $82

Answer(s): (a) $204; (b) $82