Perry and Liam were given some allowances each. If Perry spent $16 each day and Liam spent $32 each day, Perry would still have $892 left when Liam spent all his allowance. If Perry spent $32 each day and Liam spent $16 each day, Perry would still have $28 left when Liam spent all his allowance.

1. How much allowance did Perry receive?
2. How much allowance did Liam receive?

	Case 1		Case 2
	Perry	Liam	Perry	Liam
Before	1 u + 892	2 u	2 p + 28	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	892	0	28	0

(a)
Simplify the ratio.
16 : 32 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 28 = 1 u + 892
4 u - 1 u = 892 - 28
3 u = 864

1 u = 864 ÷ 3 = 288

Allowance that Perry received
= 1 u + 892
= 288 + 892
= $1180

(b)
Allowance that Liam received
= 2 u
= 2 x 288
= $576

Answers: (a) $1180; (b) $576