The sum of three consecutive integers is 72. What is the value of each integer?

Question

The sum of three consecutive integers is 72. What is the value of each integer?

Answer 1

Three consecutive numbers added together equal 72. Let's let a number, n, represent the smallest number. the number that is directly higher than this number would have to be one more than n. We can express it as "n+1". This means our largest number must be two more than our smallest number. This could be expressed as "n+2".

Now with this information we have:

n + (n+1) + (n+2) = 72

Next, let's drop the parentheses and combine like terms.

n + n + 1 + n + 2 = 72

3n + 3 = 72

Now, we have a two step equation. Let's solve for n. First work on getting the variable by itself, three is being added to it. An equation is like a balance scale. What happens to one side must happen to the other or else it will become unbalanced. With addition occurring, the inverse is what is needed in order to accomplish this. Subtract three on both sides and now the equation is:

3n = 69

The inverse of multiplication is division. Now, divide by three on both sides to find n.

n = 23.

Remember, we defined n as the smallest number. Plug it in to our original equation at the top without the equal sign and find the other two numbers.

n + (n+1) + (n+2)

23 + (23+1) + (23+2)

Then add those three numbers together to make sure that it equals the sum we were given in the problem, 72.

23 + 24 +25 = 72

72 = 72 and that's a true statement so those three numbers are the correct answer.

23, 24, and 25