Pierre and Bryan were given some allowances each. If Pierre spent $16 each day and Bryan spent $48 each day, Pierre would still have $2730 left when Bryan spent all his allowance. If Pierre spent $48 each day and Bryan spent $16 each day, Pierre would still have $42 left when Bryan spent all his allowance.

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

	Case 1		Case 2
	Pierre	Bryan	Pierre	Bryan
Before	1 u + 2730	3 u	3 p + 42	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2730	0	42	0

(a)
Simplify the ratio.
16 : 48 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 42 = 1 u + 2730
9 u - 1 u = 2730 - 42
8 u = 2688

1 u = 2688 ÷ 8 = 336

Allowance that Pierre received
= 1 u + 2730
= 336 + 2730
= $3066

(b)
Allowance that Bryan received
= 3 u
= 3 x 336
= $1008

Answers: (a) $3066; (b) $1008