Fred and Ivan were given some allowances each. If Fred spent $24 each day and Ivan spent $72 each day, Fred would still have $1368 left when Ivan spent all his allowance. If Fred spent $72 each day and Ivan spent $24 each day, Fred would still have $24 left when Ivan spent all his allowance.

1. How much allowance did Fred receive?
2. How much allowance did Ivan receive?

	Case 1		Case 2
	Fred	Ivan	Fred	Ivan
Before	1 u + 1368	3 u	3 p + 24	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1368	0	24	0

(a)
Simplify the ratio.
24 : 72 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 24 = 1 u + 1368
9 u - 1 u = 1368 - 24
8 u = 1344

1 u = 1344 ÷ 8 = 168

Allowance that Fred received
= 1 u + 1368
= 168 + 1368
= $1536

(b)
Allowance that Ivan received
= 3 u
= 3 x 168
= $504

Answers: (a) $1536; (b) $504