Vincent and Elijah were given some allowances each. If Vincent spent $13 each day and Elijah spent $26 each day, Vincent would still have $413 left when Elijah spent all his allowance. If Vincent spent $26 each day and Elijah spent $13 each day, Vincent would still have $62 left when Elijah spent all his allowance.

1. How much allowance did Vincent receive?
2. How much allowance did Elijah receive?

	Case 1		Case 2
	Vincent	Elijah	Vincent	Elijah
Before	1 u + 413	2 u	2 p + 62	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	413	0	62	0

(a)
Simplify the ratio.
13 : 26 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 62 = 1 u + 413
4 u - 1 u = 413 - 62
3 u = 351

1 u = 351 ÷ 3 = 117

Allowance that Vincent received
= 1 u + 413
= 117 + 413
= $530

(b)
Allowance that Elijah received
= 2 u
= 2 x 117
= $234

Answers: (a) $530; (b) $234