Riordan and Olivia has some money each. If Olivia gives Riordan $12, he will have 7 times as much money as her. If Riordan gives Olivia $17, he will have the same amount of money as her. How much money does each person have respectively?

1. Riordan?
2. Olivia?

	Case 1		Case 2
	Riordan	Olivia	Riordan	Olivia
Before	7 u - 12	1 u + 12	4 u + 17	4 u - 17
Change	+ 12	- 12	- 17	+ 17
After	7 u	1 u	4 u	4 u

(a)
If Olivia gives Riordan some money or Riordan gives Olivia some money, the total amount of money remains the same.  

Total amount that Riordan and Olivia have in the end for both cases
= 7 u + 1 u
= 8 u

Amount that Riordan and Olivia each has in the end in Case 2
= 8 u ÷ 2
= 4 u

The amount that Riordan has at first in Case 1 and Case 2 is the same.
7 u - 12 = 4 u + 17
7 u - 4 u = 17 + 12

1 u = 29

Amount that Riordan has
= 4 u + 17
= 4 x 29 + 17
= 116 + 17
= $133

(b)
Amount that Olivia has
= 1 u + 12
= 29 + 12
= $41

Answer(s): (a) $133; (b) $41