If Vanessa gives Mark $39, the amount of money she has will be 30% of his. If Mark gives Vanessa $136, he will have the same amount of money as her. How much money did each of them have?
(a) Mark
(b) Vanessa

	Case 1		Case 2
	Mark	Vanessa	Mark	Vanessa
Before	10 u - 39	3 u + 39	6.5 u + 136	6.5 u - 136
Change	+ 39	- 39	- 136	+ 136
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

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

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

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

10 u - 39 = 6.5 u + 136
10 u - 6.5 u = 136 + 39
3.5 u = 175 

1 u = 175 ÷ 3.5 = 50

Amount that Mark has
= 10 u - 39
= 10 x 50 - 39
= 500 - 39
= $461 

(b)
Amount that Vanessa has
= 3 u + 39
= 3 x 50 + 39
= 150 + 39
= $189

Answer(s): (a) $461; (b) $189