Reggie and Ethan were given some allowances each. If Reggie spent $29 each day and Ethan spent $87 each day, Reggie would still have $1444 left when Ethan spent all his allowance. If Reggie spent $87 each day and Ethan spent $29 each day, Reggie would still have $52 left when Ethan spent all his allowance.

1. How much allowance did Reggie receive?
2. How much allowance did Ethan receive?

	Case 1		Case 2
	Reggie	Ethan	Reggie	Ethan
Before	1 u + 1444	3 u	3 p + 52	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1444	0	52	0

(a)
Simplify the ratio.
29 : 87 = 1 : 3

The allowance that Ethan had at first is the same for Case 1 and Case 2.

1 p = 3 u
3 p = 9 u

The allowance that Reggie had at first is the same for Case 1 and Case 2.

9 u + 52 = 1 u + 1444
9 u - 1 u = 1444 - 52
8 u = 1392

1 u = 1392 ÷ 8 = 174

Allowance that Reggie received
= 1 u + 1444
= 174 + 1444
= $1618

(b)
Allowance that Ethan received
= 3 u
= 3 x 174
= $522

Answers: (a) $1618; (b) $522