Elijah and Reggie were given some allowances each. If Elijah spent $17 each day and Reggie spent $51 each day, Elijah would still have $1802 left when Reggie spent all his allowance. If Elijah spent $51 each day and Reggie spent $17 each day, Elijah would still have $34 left when Reggie spent all his allowance.

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

	Case 1		Case 2
	Elijah	Reggie	Elijah	Reggie
Before	1 u + 1802	3 u	3 p + 34	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1802	0	34	0

(a)
Simplify the ratio.
17 : 51 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 34 = 1 u + 1802
9 u - 1 u = 1802 - 34
8 u = 1768

1 u = 1768 ÷ 8 = 221

Allowance that Elijah received
= 1 u + 1802
= 221 + 1802
= $2023

(b)
Allowance that Reggie received
= 3 u
= 3 x 221
= $663

Answers: (a) $2023; (b) $663