If Gem gives Michael $21, the amount of money she has will be 30% of his. If Michael gives Gem $77, he will have the same amount of money as her. How much money did each of them have?
(a) Michael
(b) Gem

	Case 1		Case 2
	Michael	Gem	Michael	Gem
Before	10 u - 21	3 u + 21	6.5 u + 77	6.5 u - 77
Change	+ 21	- 21	- 77	+ 77
After	10 u	3 u	6.5 u	6.5 u

(a)
30% = ³⁰₁₀₀ = ³₁₀

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

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

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

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

10 u - 21 = 6.5 u + 77
10 u - 6.5 u = 77 + 21
3.5 u = 98 

1 u = 98 ÷ 3.5 = 28

Amount that Michael has
= 10 u - 21
= 10 x 28 - 21
= 280 - 21
= $259 

(b)
Amount that Gem has
= 3 u + 21
= 3 x 28 + 21
= 84 + 21
= $105

Answer(s): (a) $259; (b) $105