David and Reggie were given some allowances each. If David spent $13 each day and Reggie spent $26 each day, David would still have $1048 left when Reggie spent all his allowance. If David spent $26 each day and Reggie spent $13 each day, David would still have $34 left when Reggie spent all his allowance.

1. How much allowance did David receive?
2. How much allowance did Reggie receive?

	Case 1		Case 2
	David	Reggie	David	Reggie
Before	1 u + 1048	2 u	2 p + 34	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1048	0	34	0

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

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

1 p = 2 u
2 p = 4 u

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

4 u + 34 = 1 u + 1048
4 u - 1 u = 1048 - 34
3 u = 1014

1 u = 1014 ÷ 3 = 338

Allowance that David received
= 1 u + 1048
= 338 + 1048
= $1386

(b)
Allowance that Reggie received
= 2 u
= 2 x 338
= $676

Answers: (a) $1386; (b) $676