If Vanessa gives Caden $20, the amount of money she has will be 30% of his. If Caden gives Vanessa $78, he will have the same amount of money as her. How much money did each of them have?
(a) Caden
(b) Vanessa

	Case 1		Case 2
	Caden	Vanessa	Caden	Vanessa
Before	10 u - 20	3 u + 20	6.5 u + 78	6.5 u - 78
Change	+ 20	- 20	- 78	+ 78
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

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

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

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

10 u - 20 = 6.5 u + 78
10 u - 6.5 u = 78 + 20
3.5 u = 98 

1 u = 98 ÷ 3.5 = 28

Amount that Caden has
= 10 u - 20
= 10 x 28 - 20
= 280 - 20
= $260 

(b)
Amount that Vanessa has
= 3 u + 20
= 3 x 28 + 20
= 84 + 20
= $104

Answer(s): (a) $260; (b) $104