Question

The sum of two numbers is 95. If one number exceeds the other by 15, find the numbers.

Answer 1

Hint: This is a question of linear equations in a single variable. That is, we will assume a variable and form the equations according to what is given in the question. Then we can solve that equation using simple algebra.

Complete step-by-step solution -
It has been given that the sum of two numbers is 95. So, we will assume that the smaller number is x. It is also given that one number exceeds the other by 15, so the larger number will be x + 15.
The expression for their sum can be written as-
x + (x + 15)
It is given that their sum is 95 so-
x + (x + 15) = 95
2x = 80
x = 40
x + 15 = 55

Note: Instead of solving the question using one variable, we can use two variables and form two different equations. We will assume the numbers to be x and y. The second number exceeds the first by 15 so-
y = x + 15
Also, their sum is 95 so-
x + y = 95
Adding the two equations-
y + x + y = x + 15 + 95
2y = 110
y = 55
x = 55 - 15 = 40
We get the same answer.