The sum of five consecutive integers is 80

Book:	Competition math for middle school
Algebra:	Writing Equations
Page:	3
Writer:	Jason Batterson (J. Batterson)

Question:

The sum of five consecutive integers is 80. What is the smallest of these integers?

Answer:

It is often recommended that students label the integers x, x + 1, x + 2.x + 3, and x’+4. ‘The equation is then:
x+(x+1)+(x+2)+(x+3)+(x+4) =80
Combining like terms we get 5x + 10 = 80 or x = 14.

Do you see why it may be easier to label the middle number x in this case? It is important to remember that you are solving for the middle number this time:

(x—2)+(x-1)+x+(x+1)+(x+2) = 80

Combining like terms we get 5x = 80 or x = 16, so

the smallest number is x -2 =14.

Often, problems will involve consecutive even or odd integers, in which case each number is two bigger than the one before it: x, x +2,x+4,x+6, etc.