Caden and Bobby were given some allowances each. If Caden spent $20 each day and Bobby spent $40 each day, Caden would still have $1218 left when Bobby spent all his allowance. If Caden spent $40 each day and Bobby spent $20 each day, Caden would still have $78 left when Bobby spent all his allowance.

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

	Case 1		Case 2
	Caden	Bobby	Caden	Bobby
Before	1 u + 1218	2 u	2 p + 78	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1218	0	78	0

(a)
Simplify the ratio.
20 : 40 = 1 : 2

The allowance that Bobby 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 + 78 = 1 u + 1218
4 u - 1 u = 1218 - 78
3 u = 1140

1 u = 1140 ÷ 3 = 380

Allowance that Caden received
= 1 u + 1218
= 380 + 1218
= $1598

(b)
Allowance that Bobby received
= 2 u
= 2 x 380
= $760

Answers: (a) $1598; (b) $760