If Diana gives Paul $27, the amount of money she has will be 10% of his. If Paul gives Diana $144, he will have the same amount of money as her. How much money did each of them have?
(a) Paul
(b) Diana

	Case 1		Case 2
	Paul	Diana	Paul	Diana
Before	10 u - 27	1 u + 27	5.5 u + 144	5.5 u - 144
Change	+ 27	- 27	- 144	+ 144
After	10 u	1 u	5.5 u	5.5 u

(a)
10% = ¹⁰₁₀₀ = ¹₁₀

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

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

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

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

10 u - 27 = 5.5 u + 144
10 u - 5.5 u = 144 + 27
4.5 u = 171 

1 u = 171 ÷ 4.5 = 38

Amount that Paul has
= 10 u - 27
= 10 x 38 - 27
= 380 - 27
= $353 

(b)
Amount that Diana has
= 1 u + 27
= 1 x 38 + 27
= 38 + 27
= $65

Answer(s): (a) $353; (b) $65