Problems involving two unknowns’ quantities can be solved using the knowledge of simultaneous equations. The quantities are given lettered names and equations are constructed to describe the given facts of the problems.

Example:

1. The sum of two numbers is 8 and the difference between them is 2.

Solution

Let the first number the a and the second number be b.

A+b=8 - - - - (1)

A-b=2 - - - - (2)

Equation (1)-(2)

2b=6,                        Þb=3

Substitute b in equation2

A-b=2

a-3=2

a=2+3

2. The daily salary paid to 4 men and 3 women workers in a garden is 37 000 FRS, while the salary of 2 men and 5 women in the same garden is 29 000 frs. Find the salary of one man and one woman.

Solution

Let the salary of one man be x and the salary of one woman be y.

       1 4x+3y=37 000 - - - - (1)

       2 2x+5y=29 000 - - - - (2)

4x + 3y =37 000

-

4x + 10y= 58000

-7y=-21 000,    y=3 000

Substitute y in equation (1)

4x+3y=37 000

4x+3(3000) = 37 000

4x + 9000 = 37 000

4x = 37 000-9 000

4x = 28 000,      Þx=7 000