Rael and Justin were given some allowances each. If Rael spent $10 each day and Justin spent $20 each day, Rael would still have $770 left when Justin spent all his allowance. If Rael spent $20 each day and Justin spent $10 each day, Rael would still have $20 left when Justin spent all his allowance.

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

	Case 1		Case 2
	Rael	Justin	Rael	Justin
Before	1 u + 770	2 u	2 p + 20	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	770	0	20	0

(a)
Simplify the ratio.
10 : 20 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 20 = 1 u + 770
4 u - 1 u = 770 - 20
3 u = 750

1 u = 750 ÷ 3 = 250

Allowance that Rael received
= 1 u + 770
= 250 + 770
= $1020

(b)
Allowance that Justin received
= 2 u
= 2 x 250
= $500

Answers: (a) $1020; (b) $500