Zane and Pierre were given some allowances each. If Zane spent $14 each day and Pierre spent $42 each day, Zane would still have $2509 left when Pierre spent all his allowance. If Zane spent $42 each day and Pierre spent $14 each day, Zane would still have $45 left when Pierre spent all his allowance.

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

	Case 1		Case 2
	Zane	Pierre	Zane	Pierre
Before	1 u + 2509	3 u	3 p + 45	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2509	0	45	0

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

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

1 p = 3 u
3 p = 9 u

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

9 u + 45 = 1 u + 2509
9 u - 1 u = 2509 - 45
8 u = 2464

1 u = 2464 ÷ 8 = 308

Allowance that Zane received
= 1 u + 2509
= 308 + 2509
= $2817

(b)
Allowance that Pierre received
= 3 u
= 3 x 308
= $924

Answers: (a) $2817; (b) $924