Caden and Brandon were given some allowances each. If Caden spent $25 each day and Brandon spent $75 each day, Caden would still have $2653 left when Brandon spent all his allowance. If Caden spent $75 each day and Brandon spent $25 each day, Caden would still have $53 left when Brandon spent all his allowance.

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

	Case 1		Case 2
	Caden	Brandon	Caden	Brandon
Before	1 u + 2653	3 u	3 p + 53	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2653	0	53	0

(a)
Simplify the ratio.
25 : 75 = 1 : 3

The allowance that Brandon 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 + 53 = 1 u + 2653
9 u - 1 u = 2653 - 53
8 u = 2600

1 u = 2600 ÷ 8 = 325

Allowance that Caden received
= 1 u + 2653
= 325 + 2653
= $2978

(b)
Allowance that Brandon received
= 3 u
= 3 x 325
= $975

Answers: (a) $2978; (b) $975