Fred and Justin were given some allowances each. If Fred spent $13 each day and Justin spent $26 each day, Fred would still have $1267 left when Justin spent all his allowance. If Fred spent $26 each day and Justin spent $13 each day, Fred would still have $97 left when Justin spent all his allowance.

1. How much allowance did Fred receive?
2. How much allowance did Justin receive?

	Case 1		Case 2
	Fred	Justin	Fred	Justin
Before	1 u + 1267	2 u	2 p + 97	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	1267	0	97	0

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

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

1 p = 2 u
2 p = 4 u

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

4 u + 97 = 1 u + 1267
4 u - 1 u = 1267 - 97
3 u = 1170

1 u = 1170 ÷ 3 = 390

Allowance that Fred received
= 1 u + 1267
= 390 + 1267
= $1657

(b)
Allowance that Justin received
= 2 u
= 2 x 390
= $780

Answers: (a) $1657; (b) $780