Justin and Billy were given some allowances each. If Justin spent $14 each day and Billy spent $42 each day, Justin would still have $1152 left when Billy spent all his allowance. If Justin spent $42 each day and Billy spent $14 each day, Justin would still have $32 left when Billy spent all his allowance.

1. How much allowance did Justin receive?
2. How much allowance did Billy receive?

	Case 1		Case 2
	Justin	Billy	Justin	Billy
Before	1 u + 1152	3 u	3 p + 32	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1152	0	32	0

(a)
Simplify the ratio.
14 : 42 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 32 = 1 u + 1152
9 u - 1 u = 1152 - 32
8 u = 1120

1 u = 1120 ÷ 8 = 140

Allowance that Justin received
= 1 u + 1152
= 140 + 1152
= $1292

(b)
Allowance that Billy received
= 3 u
= 3 x 140
= $420

Answers: (a) $1292; (b) $420