The sum of four consecutive odd integers is 112 What is the

The sum of four consecutive odd integers is 112. What is the greatest of these four integers? (Given to seventh-and eighth-grade students)

Solution

we need to find the greatest of 4 odd integers if sum of 4 odd consecutive integers is 112

let assume that x is the smallest odd integer we know that x is the current odd integer then x+2 is the next odd integer , x +2+2= x+4 is the next to next odd integer and so on

assume that x is the first that is smallest odd integer of 4 integers so

x+2 is the second odd integers

x+4 is the third odd integer

x+6 is the fourth that is greatest odd integer.

as given sum of them is 112

so add the togather we have,

x + x + 2 + x + 4 + x + 6 = 112

4x + 12 = 112

4x = 100

x = 25

so smallest odd integer is 25 and greatest odd integer is x + 6 = 25 + 6 = 31