If Betty gives Jeremy $18, the amount of money she has will be 10% of his. If Jeremy gives Betty $126, he will have the same amount of money as her. How much money did each of them have?
(a) Jeremy
(b) Betty

	Case 1		Case 2
	Jeremy	Betty	Jeremy	Betty
Before	10 u - 18	1 u + 18	5.5 u + 126	5.5 u - 126
Change	+ 18	- 18	- 126	+ 126
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

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

Amount that Betty 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 - 18 = 5.5 u + 126
10 u - 5.5 u = 126 + 18
4.5 u = 144 

1 u = 144 ÷ 4.5 = 32

Amount that Jeremy has
= 10 u - 18
= 10 x 32 - 18
= 320 - 18
= $302 

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

Answer(s): (a) $302; (b) $50