Bryan and John were given some allowances each. If Bryan spent $17 each day and John spent $51 each day, Bryan would still have $1293 left when John spent all his allowance. If Bryan spent $51 each day and John spent $17 each day, Bryan would still have $69 left when John spent all his allowance.

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

	Case 1		Case 2
	Bryan	John	Bryan	John
Before	1 u + 1293	3 u	3 p + 69	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1293	0	69	0

(a)
Simplify the ratio.
17 : 51 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 69 = 1 u + 1293
9 u - 1 u = 1293 - 69
8 u = 1224

1 u = 1224 ÷ 8 = 153

Allowance that Bryan received
= 1 u + 1293
= 153 + 1293
= $1446

(b)
Allowance that John received
= 3 u
= 3 x 153
= $459

Answers: (a) $1446; (b) $459