If Jane gives Neave $23, the amount of money she has will be 25% of his. If Neave gives Jane $49, he will have the same amount of money as her. How much money did each of them have?
(a) Neave
(b) Jane

	Case 1		Case 2
	Neave	Jane	Neave	Jane
Before	4 u - 23	1 u + 23	2.5 u + 49	2.5 u - 49
Change	+ 23	- 23	- 49	+ 49
After	4 u	1 u	2.5 u	2.5 u

(a)
25% = ²⁵₁₀₀ = ¹₄

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

In Case 2, when Neave gives to Jane, there is an internal transfer of money from Neave to Jane. 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 Jane and Neave have
= 4 u + 1 u
= 5 u

Amount that Jane and Neave each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u

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

4 u - 23 = 2.5 u + 49
4 u - 2.5 u = 49 + 23
1.5 u = 72 

1 u = 72 ÷ 1.5 = 48

Amount that Neave has
= 4 u - 23
= 4 x 48 - 23
= 192 - 23
= $169 

(b)
Amount that Jane has
= 1 u + 23
= 1 x 48 + 23
= 48 + 23
= $71

Answer(s): (a) $169; (b) $71