One third of the sum of three consecutive odd integers is 91. Find the integers.

Question

3. One third of the sum of three consecutive odd integers is 91. Find the integers.

Answer 1

1/3 the sum of three consecutive odd integers is 91

3*91=273

273 is the sum of three consecutive odd integers

using arithmetic...

273/3=91

now add 2 to 91 to get 93 and subtract 2 from 91 to get 89

the integers are 89, 91, 93

using algebra...

(1/3)[x+x+2+x+4]=91

x+x+2+x+4=91*3

3x+6=273

3x=267

x=267/3

x=89, x+2=91, and x+4=93

Answer 2

There are a few different ways to solve this, but I'll go with a numerical order in this case.

Here's what we know:

(a + b + c) / 3 = 91

b = a + 2

c = a + 4

 

Now that we have values, we can put them into our equation:

(a + (a + 2) + (a + 4)) / 3 = 91

(3a + 6) / 3 = 91

 

We can factor out a 3, and that will cancel out with the 1/3 on the outside:

a + 2 = 91

a = 89

b then must be 91, and c = 93

 

Let's check:

(89 + 91 + 93)/3  = 91

273 / 3 = 91

91 = 91