Gabriel and Archie were given some allowances each. If Gabriel spent $15 each day and Archie spent $45 each day, Gabriel would still have $2563 left when Archie spent all his allowance. If Gabriel spent $45 each day and Archie spent $15 each day, Gabriel would still have $43 left when Archie spent all his allowance.

1. How much allowance did Gabriel receive?
2. How much allowance did Archie receive?

	Case 1		Case 2
	Gabriel	Archie	Gabriel	Archie
Before	1 u + 2563	3 u	3 p + 43	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2563	0	43	0

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

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

1 p = 3 u
3 p = 9 u

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

9 u + 43 = 1 u + 2563
9 u - 1 u = 2563 - 43
8 u = 2520

1 u = 2520 ÷ 8 = 315

Allowance that Gabriel received
= 1 u + 2563
= 315 + 2563
= $2878

(b)
Allowance that Archie received
= 3 u
= 3 x 315
= $945

Answers: (a) $2878; (b) $945