If Zara gives Jeremy $27, the amount of money she has will be 10% of his. If Jeremy gives Zara $144, he will have the same amount of money as her. How much money did each of them have?
(a) Jeremy
(b) Zara

	Case 1		Case 2
	Jeremy	Zara	Jeremy	Zara
Before	10 u - 27	1 u + 27	5.5 u + 144	5.5 u - 144
Change	+ 27	- 27	- 144	+ 144
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

In Case 2, when Jeremy gives to Zara, there is an internal transfer of money from Jeremy 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 Jeremy have
= 10 u + 1 u
= 11 u

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

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

10 u - 27 = 5.5 u + 144
10 u - 5.5 u = 144 + 27
4.5 u = 171 

1 u = 171 ÷ 4.5 = 38

Amount that Jeremy has
= 10 u - 27
= 10 x 38 - 27
= 380 - 27
= $353 

(b)
Amount that Zara has
= 1 u + 27
= 1 x 38 + 27
= 38 + 27
= $65

Answer(s): (a) $353; (b) $65