Liam and John were given some allowances each. If Liam spent $13 each day and John spent $39 each day, Liam would still have $2432 left when John spent all his allowance. If Liam spent $39 each day and John spent $13 each day, Liam would still have $40 left when John spent all his allowance.

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

	Case 1		Case 2
	Liam	John	Liam	John
Before	1 u + 2432	3 u	3 p + 40	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2432	0	40	0

(a)
Simplify the ratio.
13 : 39 = 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 Liam had at first is the same for Case 1 and Case 2.

9 u + 40 = 1 u + 2432
9 u - 1 u = 2432 - 40
8 u = 2392

1 u = 2392 ÷ 8 = 299

Allowance that Liam received
= 1 u + 2432
= 299 + 2432
= $2731

(b)
Allowance that John received
= 3 u
= 3 x 299
= $897

Answers: (a) $2731; (b) $897