If Tiffany gives Zeph $20, the amount of money she has will be 10% of his. If Zeph gives Tiffany $178, he will have the same amount of money as her. How much money did each of them have?
(a) Zeph
(b) Tiffany

	Case 1		Case 2
	Zeph	Tiffany	Zeph	Tiffany
Before	10 u - 20	1 u + 20	5.5 u + 178	5.5 u - 178
Change	+ 20	- 20	- 178	+ 178
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

In Case 2, when Zeph gives to Tiffany, there is an internal transfer of money from Zeph to Tiffany. 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 Tiffany and Zeph have
= 10 u + 1 u
= 11 u

Amount that Tiffany and Zeph each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u

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

10 u - 20 = 5.5 u + 178
10 u - 5.5 u = 178 + 20
4.5 u = 198 

1 u = 198 ÷ 4.5 = 44

Amount that Zeph has
= 10 u - 20
= 10 x 44 - 20
= 440 - 20
= $420 

(b)
Amount that Tiffany has
= 1 u + 20
= 1 x 44 + 20
= 44 + 20
= $64

Answer(s): (a) $420; (b) $64