Carl and Peter were given some allowances each. If Carl spent $16 each day and Peter spent $48 each day, Carl would still have $1237 left when Peter spent all his allowance. If Carl spent $48 each day and Peter spent $16 each day, Carl would still have $85 left when Peter spent all his allowance.

1. How much allowance did Carl receive?
2. How much allowance did Peter receive?

	Case 1		Case 2
	Carl	Peter	Carl	Peter
Before	1 u + 1237	3 u	3 p + 85	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1237	0	85	0

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

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

1 p = 3 u
3 p = 9 u

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

9 u + 85 = 1 u + 1237
9 u - 1 u = 1237 - 85
8 u = 1152

1 u = 1152 ÷ 8 = 144

Allowance that Carl received
= 1 u + 1237
= 144 + 1237
= $1381

(b)
Allowance that Peter received
= 3 u
= 3 x 144
= $432

Answers: (a) $1381; (b) $432