the sum of three consecutive integers is 267. What is the largest integer?

Question

The sum of three consecutive integers is 267. What is the largest integer?

Answer 1

We know that integers are whole numbers.

 

 

The smallest integer = x

The second smallest integer = x + 1

The largest integer = x + 2

 

 

Now that we have our variables, we can set up an equation that shows the sum of these integers.

 

x + (x + 1) + (x + 2) = 267

 

 

Solve for x.

 

3x + 3 = 267

 

 

Subtract 3 on both sides of the equation.

 

3x = 264

 

 

Divide both sides of the equation 3.

 

x = 88

 

 

Add 2 to this value of x to get the largest integer.

 

Answer 2

Let x be the largest integer, x-1 be the next lowest integer, and x-2 be the third integer.

 

x + x-1 + x-2 = 267

 

combine like terms:

 

3x -3 = 267

 

Isolate x by adding 3 to each side.

 

3x = 270 

 

Divide each side by 3:

 

x = 90

 

Substitute into your original equation to check:

 

90 + 89 + 88 = 267