Simon and Albert were given some allowances each. If Simon spent $17 each day and Albert spent $51 each day, Simon would still have $1448 left when Albert spent all his allowance. If Simon spent $51 each day and Albert spent $17 each day, Simon would still have $88 left when Albert spent all his allowance.

1. How much allowance did Simon receive?
2. How much allowance did Albert receive?

	Case 1		Case 2
	Simon	Albert	Simon	Albert
Before	1 u + 1448	3 u	3 p + 88	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1448	0	88	0

(a)
Simplify the ratio.
17 : 51 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 88 = 1 u + 1448
9 u - 1 u = 1448 - 88
8 u = 1360

1 u = 1360 ÷ 8 = 170

Allowance that Simon received
= 1 u + 1448
= 170 + 1448
= $1618

(b)
Allowance that Albert received
= 3 u
= 3 x 170
= $510

Answers: (a) $1618; (b) $510