Paul and Ken were given some allowances each. If Paul spent $16 each day and Ken spent $48 each day, Paul would still have $3030 left when Ken spent all his allowance. If Paul spent $48 each day and Ken spent $16 each day, Paul would still have $86 left when Ken spent all his allowance.

1. How much allowance did Paul receive?
2. How much allowance did Ken receive?

	Case 1		Case 2
	Paul	Ken	Paul	Ken
Before	1 u + 3030	3 u	3 p + 86	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	3030	0	86	0

(a)
Simplify the ratio.
16 : 48 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 86 = 1 u + 3030
9 u - 1 u = 3030 - 86
8 u = 2944

1 u = 2944 ÷ 8 = 368

Allowance that Paul received
= 1 u + 3030
= 368 + 3030
= $3398

(b)
Allowance that Ken received
= 3 u
= 3 x 368
= $1104

Answers: (a) $3398; (b) $1104