Ken and John were given some allowances each. If Ken spent $12 each day and John spent $36 each day, Ken would still have $3157 left when John spent all his allowance. If Ken spent $36 each day and John spent $12 each day, Ken would still have $85 left when John spent all his allowance.

1. How much allowance did Ken receive?
2. How much allowance did John receive?

	Case 1		Case 2
	Ken	John	Ken	John
Before	1 u + 3157	3 u	3 p + 85	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	3157	0	85	0

(a)
Simplify the ratio.
12 : 36 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 85 = 1 u + 3157
9 u - 1 u = 3157 - 85
8 u = 3072

1 u = 3072 ÷ 8 = 384

Allowance that Ken received
= 1 u + 3157
= 384 + 3157
= $3541

(b)
Allowance that John received
= 3 u
= 3 x 384
= $1152

Answers: (a) $3541; (b) $1152