If Emma gives Andy $40, the amount of money she has will be 30% of his. If Andy gives Emma $51, he will have the same amount of money as her. How much money did each of them have?
(a) Andy
(b) Emma

	Case 1		Case 2
	Andy	Emma	Andy	Emma
Before	10 u - 40	3 u + 40	6.5 u + 51	6.5 u - 51
Change	+ 40	- 40	- 51	+ 51
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

In Case 2, when Andy gives to Emma, there is an internal transfer of money from Andy to Emma. 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 Emma and Andy have
= 10 u + 3 u
= 13 u

Amount that Emma and Andy each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u

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

10 u - 40 = 6.5 u + 51
10 u - 6.5 u = 51 + 40
3.5 u = 91 

1 u = 91 ÷ 3.5 = 26

Amount that Andy has
= 10 u - 40
= 10 x 26 - 40
= 260 - 40
= $220 

(b)
Amount that Emma has
= 3 u + 40
= 3 x 26 + 40
= 78 + 40
= $118

Answer(s): (a) $220; (b) $118