Gabriel and Jeremy were given some allowances each. If Gabriel spent $22 each day and Jeremy spent $44 each day, Gabriel would still have $1090 left when Jeremy spent all his allowance. If Gabriel spent $44 each day and Jeremy spent $22 each day, Gabriel would still have $100 left when Jeremy spent all his allowance.

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

	Case 1		Case 2
	Gabriel	Jeremy	Gabriel	Jeremy
Before	1 u + 1090	2 u	2 p + 100	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1090	0	100	0

(a)
Simplify the ratio.
22 : 44 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 100 = 1 u + 1090
4 u - 1 u = 1090 - 100
3 u = 990

1 u = 990 ÷ 3 = 330

Allowance that Gabriel received
= 1 u + 1090
= 330 + 1090
= $1420

(b)
Allowance that Jeremy received
= 2 u
= 2 x 330
= $660

Answers: (a) $1420; (b) $660