Caden and Carl were given some allowances each. If Caden spent $21 each day and Carl spent $42 each day, Caden would still have $466 left when Carl spent all his allowance. If Caden spent $42 each day and Carl spent $21 each day, Caden would still have $88 left when Carl spent all his allowance.

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

	Case 1		Case 2
	Caden	Carl	Caden	Carl
Before	1 u + 466	2 u	2 p + 88	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	466	0	88	0

(a)
Simplify the ratio.
21 : 42 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 88 = 1 u + 466
4 u - 1 u = 466 - 88
3 u = 378

1 u = 378 ÷ 3 = 126

Allowance that Caden received
= 1 u + 466
= 126 + 466
= $592

(b)
Allowance that Carl received
= 2 u
= 2 x 126
= $252

Answers: (a) $592; (b) $252