Archie and Bryan were given some allowances each. If Archie spent $16 each day and Bryan spent $32 each day, Archie would still have $766 left when Bryan spent all his allowance. If Archie spent $32 each day and Bryan spent $16 each day, Archie would still have $94 left when Bryan spent all his allowance.

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

	Case 1		Case 2
	Archie	Bryan	Archie	Bryan
Before	1 u + 766	2 u	2 p + 94	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	766	0	94	0

(a)
Simplify the ratio.
16 : 32 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 94 = 1 u + 766
4 u - 1 u = 766 - 94
3 u = 672

1 u = 672 ÷ 3 = 224

Allowance that Archie received
= 1 u + 766
= 224 + 766
= $990

(b)
Allowance that Bryan received
= 2 u
= 2 x 224
= $448

Answers: (a) $990; (b) $448