Andy and Rael were given some allowances each. If Andy spent $19 each day and Rael spent $38 each day, Andy would still have $1017 left when Rael spent all his allowance. If Andy spent $38 each day and Rael spent $19 each day, Andy would still have $48 left when Rael spent all his allowance.

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

	Case 1		Case 2
	Andy	Rael	Andy	Rael
Before	1 u + 1017	2 u	2 p + 48	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1017	0	48	0

(a)
Simplify the ratio.
19 : 38 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 48 = 1 u + 1017
4 u - 1 u = 1017 - 48
3 u = 969

1 u = 969 ÷ 3 = 323

Allowance that Andy received
= 1 u + 1017
= 323 + 1017
= $1340

(b)
Allowance that Rael received
= 2 u
= 2 x 323
= $646

Answers: (a) $1340; (b) $646