If Dana gives Ian $27, the amount of money she has will be 10% of his. If Ian gives Dana $99, he will have the same amount of money as her. How much money did each of them have?
(a) Ian
(b) Dana

	Case 1		Case 2
	Ian	Dana	Ian	Dana
Before	10 u - 27	1 u + 27	5.5 u + 99	5.5 u - 99
Change	+ 27	- 27	- 99	+ 99
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

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

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

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

10 u - 27 = 5.5 u + 99
10 u - 5.5 u = 99 + 27
4.5 u = 126 

1 u = 126 ÷ 4.5 = 28

Amount that Ian has
= 10 u - 27
= 10 x 28 - 27
= 280 - 27
= $253 

(b)
Amount that Dana has
= 1 u + 27
= 1 x 28 + 27
= 28 + 27
= $55

Answer(s): (a) $253; (b) $55