Pierre and Opal has some money each. If Opal gives Pierre $13, he will have 7 times as much money as her. If Pierre gives Opal $19, he will have the same amount of money as her. How much money does each person have respectively?

1. Pierre?
2. Opal?

	Case 1		Case 2
	Pierre	Opal	Pierre	Opal
Before	7 u - 13	1 u + 13	4 u + 19	4 u - 19
Change	+ 13	- 13	- 19	+ 19
After	7 u	1 u	4 u	4 u

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

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

Amount that Pierre and Opal each has in the end in Case 2
= 8 u ÷ 2
= 4 u

The amount that Pierre has at first in Case 1 and Case 2 is the same.
7 u - 13 = 4 u + 19
7 u - 4 u = 19 + 13

1 u = 32

Amount that Pierre has
= 4 u + 19
= 4 x 32 + 19
= 128 + 19
= $147

(b)
Amount that Opal has
= 1 u + 13
= 32 + 13
= $45

Answer(s): (a) $147; (b) $45