Ben and Rael were given some allowances each. If Ben spent $14 each day and Rael spent $28 each day, Ben would still have $379 left when Rael spent all his allowance. If Ben spent $28 each day and Rael spent $14 each day, Ben would still have $43 left when Rael spent all his allowance.

1. How much allowance did Ben receive?
2. How much allowance did Rael receive?

	Case 1		Case 2
	Ben	Rael	Ben	Rael
Before	1 u + 379	2 u	2 p + 43	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	379	0	43	0

(a)
Simplify the ratio.
14 : 28 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 43 = 1 u + 379
4 u - 1 u = 379 - 43
3 u = 336

1 u = 336 ÷ 3 = 112

Allowance that Ben received
= 1 u + 379
= 112 + 379
= $491

(b)
Allowance that Rael received
= 2 u
= 2 x 112
= $224

Answers: (a) $491; (b) $224