Asher and Justin were given some allowances each. If Asher spent $10 each day and Justin spent $30 each day, Asher would still have $3105 left when Justin spent all his allowance. If Asher spent $30 each day and Justin spent $10 each day, Asher would still have $65 left when Justin spent all his allowance.

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

	Case 1		Case 2
	Asher	Justin	Asher	Justin
Before	1 u + 3105	3 u	3 p + 65	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	3105	0	65	0

(a)
Simplify the ratio.
10 : 30 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 65 = 1 u + 3105
9 u - 1 u = 3105 - 65
8 u = 3040

1 u = 3040 ÷ 8 = 380

Allowance that Asher received
= 1 u + 3105
= 380 + 3105
= $3485

(b)
Allowance that Justin received
= 3 u
= 3 x 380
= $1140

Answers: (a) $3485; (b) $1140