George and Brandon were given some allowances each. If George spent $18 each day and Brandon spent $54 each day, George would still have $1958 left when Brandon spent all his allowance. If George spent $54 each day and Brandon spent $18 each day, George would still have $86 left when Brandon spent all his allowance.

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

	Case 1		Case 2
	George	Brandon	George	Brandon
Before	1 u + 1958	3 u	3 p + 86	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1958	0	86	0

(a)
Simplify the ratio.
18 : 54 = 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 George had at first is the same for Case 1 and Case 2.

9 u + 86 = 1 u + 1958
9 u - 1 u = 1958 - 86
8 u = 1872

1 u = 1872 ÷ 8 = 234

Allowance that George received
= 1 u + 1958
= 234 + 1958
= $2192

(b)
Allowance that Brandon received
= 3 u
= 3 x 234
= $702

Answers: (a) $2192; (b) $702