Ivan and Ethan were given some allowances each. If Ivan spent $30 each day and Ethan spent $90 each day, Ivan would still have $2929 left when Ethan spent all his allowance. If Ivan spent $90 each day and Ethan spent $30 each day, Ivan would still have $49 left when Ethan spent all his allowance.

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

	Case 1		Case 2
	Ivan	Ethan	Ivan	Ethan
Before	1 u + 2929	3 u	3 p + 49	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2929	0	49	0

(a)
Simplify the ratio.
30 : 90 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 49 = 1 u + 2929
9 u - 1 u = 2929 - 49
8 u = 2880

1 u = 2880 ÷ 8 = 360

Allowance that Ivan received
= 1 u + 2929
= 360 + 2929
= $3289

(b)
Allowance that Ethan received
= 3 u
= 3 x 360
= $1080

Answers: (a) $3289; (b) $1080