Charlie and Ivan were given some allowances each. If Charlie spent $20 each day and Ivan spent $40 each day, Charlie would still have $1251 left when Ivan spent all his allowance. If Charlie spent $40 each day and Ivan spent $20 each day, Charlie would still have $51 left when Ivan spent all his allowance.

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

	Case 1		Case 2
	Charlie	Ivan	Charlie	Ivan
Before	1 u + 1251	2 u	2 p + 51	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1251	0	51	0

(a)
Simplify the ratio.
20 : 40 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 51 = 1 u + 1251
4 u - 1 u = 1251 - 51
3 u = 1200

1 u = 1200 ÷ 3 = 400

Allowance that Charlie received
= 1 u + 1251
= 400 + 1251
= $1651

(b)
Allowance that Ivan received
= 2 u
= 2 x 400
= $800

Answers: (a) $1651; (b) $800