Ryan and Zane were given some allowances each. If Ryan spent $27 each day and Zane spent $81 each day, Ryan would still have $1172 left when Zane spent all his allowance. If Ryan spent $81 each day and Zane spent $27 each day, Ryan would still have $92 left when Zane spent all his allowance.

1. How much allowance did Ryan receive?
2. How much allowance did Zane receive?

	Case 1		Case 2
	Ryan	Zane	Ryan	Zane
Before	1 u + 1172	3 u	3 p + 92	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1172	0	92	0

(a)
Simplify the ratio.
27 : 81 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 92 = 1 u + 1172
9 u - 1 u = 1172 - 92
8 u = 1080

1 u = 1080 ÷ 8 = 135

Allowance that Ryan received
= 1 u + 1172
= 135 + 1172
= $1307

(b)
Allowance that Zane received
= 3 u
= 3 x 135
= $405

Answers: (a) $1307; (b) $405