If Zara gives Howard $18, the amount of money she has will be 25% of his. If Howard gives Zara $30, he will have the same amount of money as her. How much money did each of them have?
(a) Howard
(b) Zara

	Case 1		Case 2
	Howard	Zara	Howard	Zara
Before	4 u - 18	1 u + 18	2.5 u + 30	2.5 u - 30
Change	+ 18	- 18	- 30	+ 30
After	4 u	1 u	2.5 u	2.5 u

(a)
25% = ²⁵₁₀₀ = ¹₄

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

In Case 2, when Howard gives to Zara, there is an internal transfer of money from Howard to Zara. 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 Zara and Howard have
= 4 u + 1 u
= 5 u

Amount that Zara and Howard each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u

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

4 u - 18 = 2.5 u + 30
4 u - 2.5 u = 30 + 18
1.5 u = 48 

1 u = 48 ÷ 1.5 = 32

Amount that Howard has
= 4 u - 18
= 4 x 32 - 18
= 128 - 18
= $110 

(b)
Amount that Zara has
= 1 u + 18
= 1 x 32 + 18
= 32 + 18
= $50

Answer(s): (a) $110; (b) $50