Michael and Jack were given some allowances each. If Michael spent $21 each day and Jack spent $42 each day, Michael would still have $374 left when Jack spent all his allowance. If Michael spent $42 each day and Jack spent $21 each day, Michael would still have $59 left when Jack spent all his allowance.

1. How much allowance did Michael receive?
2. How much allowance did Jack receive?

	Case 1		Case 2
	Michael	Jack	Michael	Jack
Before	1 u + 374	2 u	2 p + 59	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	374	0	59	0

(a)
Simplify the ratio.
21 : 42 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 59 = 1 u + 374
4 u - 1 u = 374 - 59
3 u = 315

1 u = 315 ÷ 3 = 105

Allowance that Michael received
= 1 u + 374
= 105 + 374
= $479

(b)
Allowance that Jack received
= 2 u
= 2 x 105
= $210

Answers: (a) $479; (b) $210