John and Luis were given some allowances each. If John spent $17 each day and Luis spent $51 each day, John would still have $2124 left when Luis spent all his allowance. If John spent $51 each day and Luis spent $17 each day, John would still have $84 left when Luis spent all his allowance.

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

	Case 1		Case 2
	John	Luis	John	Luis
Before	1 u + 2124	3 u	3 p + 84	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2124	0	84	0

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

The allowance that Luis 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 + 84 = 1 u + 2124
9 u - 1 u = 2124 - 84
8 u = 2040

1 u = 2040 ÷ 8 = 255

Allowance that John received
= 1 u + 2124
= 255 + 2124
= $2379

(b)
Allowance that Luis received
= 3 u
= 3 x 255
= $765

Answers: (a) $2379; (b) $765