If Emily gives Fred $32, the amount of money she has will be 10% of his. If Fred gives Emily $175, he will have the same amount of money as her. How much money did each of them have?
(a) Fred
(b) Emily

	Case 1		Case 2
	Fred	Emily	Fred	Emily
Before	10 u - 32	1 u + 32	5.5 u + 175	5.5 u - 175
Change	+ 32	- 32	- 175	+ 175
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

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

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

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

10 u - 32 = 5.5 u + 175
10 u - 5.5 u = 175 + 32
4.5 u = 207 

1 u = 207 ÷ 4.5 = 46

Amount that Fred has
= 10 u - 32
= 10 x 46 - 32
= 460 - 32
= $428 

(b)
Amount that Emily has
= 1 u + 32
= 1 x 46 + 32
= 46 + 32
= $78

Answer(s): (a) $428; (b) $78