Answer: 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.
