Archie and Julian were given some allowances each. If Archie spent $29 each day and Julian spent $58 each day, Archie would still have $750 left when Julian spent all his allowance. If Archie spent $58 each day and Julian spent $29 each day, Archie would still have $54 left when Julian spent all his allowance.

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

	Case 1		Case 2
	Archie	Julian	Archie	Julian
Before	1 u + 750	2 u	2 p + 54	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	750	0	54	0

(a)
Simplify the ratio.
29 : 58 = 1 : 2

The allowance that Julian 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 + 54 = 1 u + 750
4 u - 1 u = 750 - 54
3 u = 696

1 u = 696 ÷ 3 = 232

Allowance that Archie received
= 1 u + 750
= 232 + 750
= $982

(b)
Allowance that Julian received
= 2 u
= 2 x 232
= $464

Answers: (a) $982; (b) $464