Question

The sum of three consecutive odd integers is 48, how do you find the largest integer?

Answer 1

The question has the wrong value as the sum. Summing 3 odd numbers will give an odd sum. However; the method is demonstrated through an example

Explanation:

Just to make this work lets derive the sum first. Suppose we had

`9+11+13=33` as our initial odd number

Let the fist odd number be `n`

Then the second odd number is `n+2`

Then the third odd number is `n+4`

So we have:

`n+(n+2)+(n+4)=33`

`3n+6=33`

Subtract 6 from both sides

`3n=27`

Divide both sides by 3

`n=9`

So the largest number is `9+4=13`

Answer 2

Explanation below.

Explanation:

The question is worded incorrectly because there are not three consecutive odd integers that add up to `48`.

What I can do for you is leave you with this method of solving this problem. Let's say I was looking for 3 consecutive integers that add up to `81`.

My first integer would be `2x-1`
My second integer would be `2x+1`
My third integer would be `2x+3`

So my equation is...

`2x-1+2x+1+2x+3=81`

Add/Subtract common terms

`6x+3=81`

`6x=81-3`

`6x=78`

`cancel6x/cancel6=78/6`

`x=13`

Now we know the value of `x` so we plug it into our 3 equations.

My first integer would be `2(13)-1` `--->` `=25`
My second integer would be `2(13)+1` `--->` `=27`
My third integer would be `2(13)+3` `--->` `=29`

So,

`25+27+29=81`