Glen and Archie were given some allowances each. If Glen spent $17 each day and Archie spent $34 each day, Glen would still have $1021 left when Archie spent all his allowance. If Glen spent $34 each day and Archie spent $17 each day, Glen would still have $52 left when Archie spent all his allowance.

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

	Case 1		Case 2
	Glen	Archie	Glen	Archie
Before	1 u + 1021	2 u	2 p + 52	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1021	0	52	0

(a)
Simplify the ratio.
17 : 34 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 52 = 1 u + 1021
4 u - 1 u = 1021 - 52
3 u = 969

1 u = 969 ÷ 3 = 323

Allowance that Glen received
= 1 u + 1021
= 323 + 1021
= $1344

(b)
Allowance that Archie received
= 2 u
= 2 x 323
= $646

Answers: (a) $1344; (b) $646