If Betty gives Simon $28, the amount of money she has will be 10% of his. If Simon gives Betty $125, he will have the same amount of money as her. How much money did each of them have?
(a) Simon
(b) Betty

	Case 1		Case 2
	Simon	Betty	Simon	Betty
Before	10 u - 28	1 u + 28	5.5 u + 125	5.5 u - 125
Change	+ 28	- 28	- 125	+ 125
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

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

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

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

10 u - 28 = 5.5 u + 125
10 u - 5.5 u = 125 + 28
4.5 u = 153 

1 u = 153 ÷ 4.5 = 34

Amount that Simon has
= 10 u - 28
= 10 x 34 - 28
= 340 - 28
= $312 

(b)
Amount that Betty has
= 1 u + 28
= 1 x 34 + 28
= 34 + 28
= $62

Answer(s): (a) $312; (b) $62