Simon and Jeremy were given some allowances each. If Simon spent $16 each day and Jeremy spent $48 each day, Simon would still have $2838 left when Jeremy spent all his allowance. If Simon spent $48 each day and Jeremy spent $16 each day, Simon would still have $22 left when Jeremy spent all his allowance.

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

	Case 1		Case 2
	Simon	Jeremy	Simon	Jeremy
Before	1 u + 2838	3 u	3 p + 22	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2838	0	22	0

(a)
Simplify the ratio.
16 : 48 = 1 : 3

The allowance that Jeremy 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 + 22 = 1 u + 2838
9 u - 1 u = 2838 - 22
8 u = 2816

1 u = 2816 ÷ 8 = 352

Allowance that Simon received
= 1 u + 2838
= 352 + 2838
= $3190

(b)
Allowance that Jeremy received
= 3 u
= 3 x 352
= $1056

Answers: (a) $3190; (b) $1056