If Erika gives Ethan $36, the amount of money she has will be 30% of his. If Ethan gives Erika $118, he will have the same amount of money as her. How much money did each of them have?
(a) Ethan
(b) Erika

	Case 1		Case 2
	Ethan	Erika	Ethan	Erika
Before	10 u - 36	3 u + 36	6.5 u + 118	6.5 u - 118
Change	+ 36	- 36	- 118	+ 118
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

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

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

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

10 u - 36 = 6.5 u + 118
10 u - 6.5 u = 118 + 36
3.5 u = 154 

1 u = 154 ÷ 3.5 = 44

Amount that Ethan has
= 10 u - 36
= 10 x 44 - 36
= 440 - 36
= $404 

(b)
Amount that Erika has
= 3 u + 36
= 3 x 44 + 36
= 132 + 36
= $168

Answer(s): (a) $404; (b) $168