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.