Albert and Henry were given some allowances each. If Albert spent $12 each day and Henry spent $36 each day, Albert would still have $1614 left when Henry spent all his allowance. If Albert spent $36 each day and Henry spent $12 each day, Albert would still have $78 left when Henry spent all his allowance.

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

	Case 1		Case 2
	Albert	Henry	Albert	Henry
Before	1 u + 1614	3 u	3 p + 78	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1614	0	78	0

(a)
Simplify the ratio.
12 : 36 = 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 Albert had at first is the same for Case 1 and Case 2.

9 u + 78 = 1 u + 1614
9 u - 1 u = 1614 - 78
8 u = 1536

1 u = 1536 ÷ 8 = 192

Allowance that Albert received
= 1 u + 1614
= 192 + 1614
= $1806

(b)
Allowance that Henry received
= 3 u
= 3 x 192
= $576

Answers: (a) $1806; (b) $576