Rael and Luis were given some allowances each. If Rael spent $10 each day and Luis spent $20 each day, Rael would still have $1086 left when Luis spent all his allowance. If Rael spent $20 each day and Luis spent $10 each day, Rael would still have $36 left when Luis spent all his allowance.

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

	Case 1		Case 2
	Rael	Luis	Rael	Luis
Before	1 u + 1086	2 u	2 p + 36	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1086	0	36	0

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

The allowance that Luis 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 + 36 = 1 u + 1086
4 u - 1 u = 1086 - 36
3 u = 1050

1 u = 1050 ÷ 3 = 350

Allowance that Rael received
= 1 u + 1086
= 350 + 1086
= $1436

(b)
Allowance that Luis received
= 2 u
= 2 x 350
= $700

Answers: (a) $1436; (b) $700