Flynn and Luke were given some allowances each. If Flynn spent $10 each day and Luke spent $30 each day, Flynn would still have $2747 left when Luke spent all his allowance. If Flynn spent $30 each day and Luke spent $10 each day, Flynn would still have $27 left when Luke spent all his allowance.

1. How much allowance did Flynn receive?
2. How much allowance did Luke receive?

	Case 1		Case 2
	Flynn	Luke	Flynn	Luke
Before	1 u + 2747	3 u	3 p + 27	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2747	0	27	0

(a)
Simplify the ratio.
10 : 30 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 27 = 1 u + 2747
9 u - 1 u = 2747 - 27
8 u = 2720

1 u = 2720 ÷ 8 = 340

Allowance that Flynn received
= 1 u + 2747
= 340 + 2747
= $3087

(b)
Allowance that Luke received
= 3 u
= 3 x 340
= $1020

Answers: (a) $3087; (b) $1020