Mark and Asher were given some allowances each. If Mark spent $15 each day and Asher spent $45 each day, Mark would still have $1112 left when Asher spent all his allowance. If Mark spent $45 each day and Asher spent $15 each day, Mark would still have $32 left when Asher spent all his allowance.

1. How much allowance did Mark receive?
2. How much allowance did Asher receive?

	Case 1		Case 2
	Mark	Asher	Mark	Asher
Before	1 u + 1112	3 u	3 p + 32	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1112	0	32	0

(a)
Simplify the ratio.
15 : 45 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 32 = 1 u + 1112
9 u - 1 u = 1112 - 32
8 u = 1080

1 u = 1080 ÷ 8 = 135

Allowance that Mark received
= 1 u + 1112
= 135 + 1112
= $1247

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

Answers: (a) $1247; (b) $405