The sum of two numbers is 33. Their difference is 23. Find the numbers.

The numbers are 28 and 5

Step-by-step explanation: The question gives a set of clues. In the first instance, the addition of two numbers equals 33. Let us assume the two numbers are A and B. What that means is that

A + B = 33.

We shall call this equation 1.

The other clue is given as “their difference is 23.” This can be expressed as

A - B = 23.

We shall call this equation 2.

Now we have a pair of simultaneous equations as follows

A + B = 33 —————-(1)

A - B = 23 —————-(2)

We shall use the substitution method

From equation (1), if we make A the subject of the equation we shall move B to the other side and we’ll have

A = 33 - B

Substitute for the value of A in equation (2)

A - B = 23 now becomes

(33 - B) - B = 23

33 - B - B = 23

33 - 2B = 23

By collecting like terms we now have 33 - 23 = 2B

(Remember that when a positive value crosses to the other side of an equation, it becomes negative, and vice versa)

33 - 23 = 2B

10 = 2B

Divide both sides of the equation by 2

5 = B

If we calculate B as 5

We can substitute for this value into equation 1, which is

A + B = 33

A + 5 = 33

Subtract 5 from both sides of the equation

A + 5 - 5 = 33 - 5

A = 28.

Therefore the numbers are 28 and 5.