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

larger number

smaller number

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].