Howard and David were given some allowances each. If Howard spent $27 each day and David spent $54 each day, Howard would still have $1228 left when David spent all his allowance. If Howard spent $54 each day and David spent $27 each day, Howard would still have $94 left when David spent all his allowance.

1. How much allowance did Howard receive?
2. How much allowance did David receive?

	Case 1		Case 2
	Howard	David	Howard	David
Before	1 u + 1228	2 u	2 p + 94	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1228	0	94	0

(a)
Simplify the ratio.
27 : 54 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 94 = 1 u + 1228
4 u - 1 u = 1228 - 94
3 u = 1134

1 u = 1134 ÷ 3 = 378

Allowance that Howard received
= 1 u + 1228
= 378 + 1228
= $1606

(b)
Allowance that David received
= 2 u
= 2 x 378
= $756

Answers: (a) $1606; (b) $756