Gabriel and Perry were given some allowances each. If Gabriel spent $13 each day and Perry spent $39 each day, Gabriel would still have $1007 left when Perry spent all his allowance. If Gabriel spent $39 each day and Perry spent $13 each day, Gabriel would still have $71 left when Perry spent all his allowance.

1. How much allowance did Gabriel receive?
2. How much allowance did Perry receive?

	Case 1		Case 2
	Gabriel	Perry	Gabriel	Perry
Before	1 u + 1007	3 u	3 p + 71	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1007	0	71	0

(a)
Simplify the ratio.
13 : 39 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 71 = 1 u + 1007
9 u - 1 u = 1007 - 71
8 u = 936

1 u = 936 ÷ 8 = 117

Allowance that Gabriel received
= 1 u + 1007
= 117 + 1007
= $1124

(b)
Allowance that Perry received
= 3 u
= 3 x 117
= $351

Answers: (a) $1124; (b) $351