Bryan and Ivan were given some allowances each. If Bryan spent $11 each day and Ivan spent $33 each day, Bryan would still have $3225 left when Ivan spent all his allowance. If Bryan spent $33 each day and Ivan spent $11 each day, Bryan would still have $57 left when Ivan spent all his allowance.

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

	Case 1		Case 2
	Bryan	Ivan	Bryan	Ivan
Before	1 u + 3225	3 u	3 p + 57	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	3225	0	57	0

(a)
Simplify the ratio.
11 : 33 = 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 Bryan had at first is the same for Case 1 and Case 2.

9 u + 57 = 1 u + 3225
9 u - 1 u = 3225 - 57
8 u = 3168

1 u = 3168 ÷ 8 = 396

Allowance that Bryan received
= 1 u + 3225
= 396 + 3225
= $3621

(b)
Allowance that Ivan received
= 3 u
= 3 x 396
= $1188

Answers: (a) $3621; (b) $1188