John and Rael were given some allowances each. If John spent $26 each day and Rael spent $78 each day, John would still have $2748 left when Rael spent all his allowance. If John spent $78 each day and Rael spent $26 each day, John would still have $44 left when Rael spent all his allowance.

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

	Case 1		Case 2
	John	Rael	John	Rael
Before	1 u + 2748	3 u	3 p + 44	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2748	0	44	0

(a)
Simplify the ratio.
26 : 78 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 44 = 1 u + 2748
9 u - 1 u = 2748 - 44
8 u = 2704

1 u = 2704 ÷ 8 = 338

Allowance that John received
= 1 u + 2748
= 338 + 2748
= $3086

(b)
Allowance that Rael received
= 3 u
= 3 x 338
= $1014

Answers: (a) $3086; (b) $1014