Caden and Henry were given some allowances each. If Caden spent $23 each day and Henry spent $69 each day, Caden would still have $3193 left when Henry spent all his allowance. If Caden spent $69 each day and Henry spent $23 each day, Caden would still have $65 left when Henry spent all his allowance.

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

	Case 1		Case 2
	Caden	Henry	Caden	Henry
Before	1 u + 3193	3 u	3 p + 65	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	3193	0	65	0

(a)
Simplify the ratio.
23 : 69 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 65 = 1 u + 3193
9 u - 1 u = 3193 - 65
8 u = 3128

1 u = 3128 ÷ 8 = 391

Allowance that Caden received
= 1 u + 3193
= 391 + 3193
= $3584

(b)
Allowance that Henry received
= 3 u
= 3 x 391
= $1173

Answers: (a) $3584; (b) $1173