Question

The sum of two numbers is 53 and the difference is 11. What are the numbers?

larger number
smaller number

Answer 1

Let assume that the the two numbers are X and Y and that X is the large number.
According to the question,
X + Y = 53 .................. Equation 1
then, X = 11 + Y........... Equation 2
Substitute equation 2 into equation 1.
[11 + Y] + Y = 53
11 + 2Y = 53
2Y = 53 - 11 = 42
2Y = 42
Y = 42 / 2 = 21,
Therefore, Y = 21 [Small number].
According to equation 1,
X +Y = 53
X + 21 = 53
X = 53 - 21 = 32.
Therefore, X = 32 [Big number].