Find two numbers whose sum is 92 and whose difference is 28.

The two unknowns:
the two numbers.

The two relationships:
Use the two relationships to set up an equation or a system of two equations.

(1)

[ the first number ] + [ the second number ] = 92

(2)

[ the first number ] - [ the second number ] = 28

Depending on how the two relationships are used, the problem can be solved by setting up either:
a system of two equations, or
one equation in one variable.

Step 1
Let x represent the first number.

Step 2
Express the second number in terms of x using relationship (1).
the second number = 92 - x

Step 3
Use relationship (2) to set up an equation.
 

[ the first number ] - [ the second number ] = 28

x - (92 - x) = 28

Step 4
Solve the equation for x.
x - (92 - x) = 28
x - 92 + x = 28
2x - 92 = 28
2x = 120
x = 60

So the first number is 60, the second one is 92 - x = 92 - 60 = 32.

Step 1
Let x represent the first number.
Let y represent the second number.

Step 2
Use relationship (1) to set up the first equation.
x + y = 92
Use relationship (2) to set up the second equation.
x - y = 28

Step 3
Solve the simultaneous equations for x and y.
x + y = 92    .....................(1)
x - y = 28     .....................(2)

Adding (1) and (2) together, we have
x + y + x - y = 92 + 28
2x = 120

Solving for x, we get
x = 60

Substituting x = 60 into equation (1), we have
60 + y = 92

Solving for y, we obtain
y = 32

The solution to the simultaneous equation is
x = 60
y = 32

So the first number is 60, the second one is 32.