Perry and Bobby were given some allowances each. If Perry spent $13 each day and Bobby spent $39 each day, Perry would still have $3158 left when Bobby spent all his allowance. If Perry spent $39 each day and Bobby spent $13 each day, Perry would still have $38 left when Bobby spent all his allowance.

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

	Case 1		Case 2
	Perry	Bobby	Perry	Bobby
Before	1 u + 3158	3 u	3 p + 38	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	3158	0	38	0

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

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

1 p = 3 u
3 p = 9 u

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

9 u + 38 = 1 u + 3158
9 u - 1 u = 3158 - 38
8 u = 3120

1 u = 3120 ÷ 8 = 390

Allowance that Perry received
= 1 u + 3158
= 390 + 3158
= $3548

(b)
Allowance that Bobby received
= 3 u
= 3 x 390
= $1170

Answers: (a) $3548; (b) $1170