Riordan and Hilda has some money each. If Hilda gives Riordan $10, he will have 7 times as much money as her. If Riordan gives Hilda $19, he will have the same amount of money as her. How much money does each person have respectively?

1. Riordan?
2. Hilda?

	Case 1		Case 2
	Riordan	Hilda	Riordan	Hilda
Before	7 u - 10	1 u + 10	4 u + 19	4 u - 19
Change	+ 10	- 10	- 19	+ 19
After	7 u	1 u	4 u	4 u

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

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

Amount that Riordan and Hilda 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 - 10 = 4 u + 19
7 u - 4 u = 19 + 10

1 u = 29

Amount that Riordan has
= 4 u + 19
= 4 x 29 + 19
= 116 + 19
= $135

(b)
Amount that Hilda has
= 1 u + 10
= 29 + 10
= $39

Answer(s): (a) $135; (b) $39