The sum of two consecutive integers is 101. What are the numbers?

Question

The sum of two consecutive integers is 101. What are the numbers?

Answer 1

Let the integers be. x and x+1

Then x + (x+1) = 101

2x = 100

x = 50

The integers are 50 and 51.

Answer 2

For this sort of question, we want to start off by asking what two consecutive numbers looks like algebraically. Some examples of consecutive numbers are 1 and 2, 6 and 7, 100 and 101, and so on. Noticing the pattern, it is simply a number and that same number plus 1. We can write this as:

n and (n+1)

We're asked to find what these two would be if their sum were 101. So we can make an equation for this:

n + (n+1) = 101

Simplifying this equation by combining the like terms, we get:

2n+1=101, subtract by 1 on both sides:

2n=100, divide by 2 on both sides:

n=50

Then our two consecutive numbers that sum to 101 are 50 and 50+1 or 50 and 51. You can add these together and see that they do indeed add up to 101.

Great question, Peg!