Vincent and Ahmad were given some allowances each. If Vincent spent $20 each day and Ahmad spent $60 each day, Vincent would still have $1051 left when Ahmad spent all his allowance. If Vincent spent $60 each day and Ahmad spent $20 each day, Vincent would still have $91 left when Ahmad spent all his allowance.

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

	Case 1		Case 2
	Vincent	Ahmad	Vincent	Ahmad
Before	1 u + 1051	3 u	3 p + 91	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1051	0	91	0

(a)
Simplify the ratio.
20 : 60 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 91 = 1 u + 1051
9 u - 1 u = 1051 - 91
8 u = 960

1 u = 960 ÷ 8 = 120

Allowance that Vincent received
= 1 u + 1051
= 120 + 1051
= $1171

(b)
Allowance that Ahmad received
= 3 u
= 3 x 120
= $360

Answers: (a) $1171; (b) $360