The sum of two numbers is 47 and the difference is 19. What are the numbers?

Answer: The two numbers are 33 and 14

Step-by-step explanation: We shall start by first assigning letters to unknown variables. Therefore let the two numbers be called a and b. The first clue in this question states that the sum of both a and b equals 47. That means we can write the expression;

a + b = 47.

The second clue states that their difference equals 19. This also can be expressed as follows;

a - b = 19

Now we have a pair of simultaneous equations which are

a + b = 47 - - - (1)

a - b = 19 - -- - (2)

We shall use the substitution method. Therefore from equation (1), make a the subject of the equation.

a = 47 - b

Next we substitute for the value of a in equation (2)

a - b = 19

47 - b - b = 19

47 - 2b = 19

By collecting like terms we now have 47 - 19 = 2b

28 = 2b

Divide both sides of the equation by 2

14 = b

We can now substitute for the value of b into equation (1)

a + b = 47

a + 14 = 47

Subtract 14 from both sides of the equation

a = 33.

Therefore the two numbers are 33 and 14.