Rael and Nick were given some allowances each. If Rael spent $25 each day and Nick spent $50 each day, Rael would still have $1161 left when Nick spent all his allowance. If Rael spent $50 each day and Nick spent $25 each day, Rael would still have $36 left when Nick spent all his allowance.

1. How much allowance did Rael receive?
2. How much allowance did Nick receive?

	Case 1		Case 2
	Rael	Nick	Rael	Nick
Before	1 u + 1161	2 u	2 p + 36	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1161	0	36	0

(a)
Simplify the ratio.
25 : 50 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 36 = 1 u + 1161
4 u - 1 u = 1161 - 36
3 u = 1125

1 u = 1125 ÷ 3 = 375

Allowance that Rael received
= 1 u + 1161
= 375 + 1161
= $1536

(b)
Allowance that Nick received
= 2 u
= 2 x 375
= $750

Answers: (a) $1536; (b) $750