Ian and Pierre were given some allowances each. If Ian spent $24 each day and Pierre spent $72 each day, Ian would still have $1195 left when Pierre spent all his allowance. If Ian spent $72 each day and Pierre spent $24 each day, Ian would still have $43 left when Pierre spent all his allowance.

1. How much allowance did Ian receive?
2. How much allowance did Pierre receive?

	Case 1		Case 2
	Ian	Pierre	Ian	Pierre
Before	1 u + 1195	3 u	3 p + 43	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1195	0	43	0

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

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

1 p = 3 u
3 p = 9 u

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

9 u + 43 = 1 u + 1195
9 u - 1 u = 1195 - 43
8 u = 1152

1 u = 1152 ÷ 8 = 144

Allowance that Ian received
= 1 u + 1195
= 144 + 1195
= $1339

(b)
Allowance that Pierre received
= 3 u
= 3 x 144
= $432

Answers: (a) $1339; (b) $432