Jeremy and Asher were given some allowances each. If Jeremy spent $30 each day and Asher spent $90 each day, Jeremy would still have $1702 left when Asher spent all his allowance. If Jeremy spent $90 each day and Asher spent $30 each day, Jeremy would still have $22 left when Asher spent all his allowance.

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

	Case 1		Case 2
	Jeremy	Asher	Jeremy	Asher
Before	1 u + 1702	3 u	3 p + 22	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1702	0	22	0

(a)
Simplify the ratio.
30 : 90 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 22 = 1 u + 1702
9 u - 1 u = 1702 - 22
8 u = 1680

1 u = 1680 ÷ 8 = 210

Allowance that Jeremy received
= 1 u + 1702
= 210 + 1702
= $1912

(b)
Allowance that Asher received
= 3 u
= 3 x 210
= $630

Answers: (a) $1912; (b) $630