Three consecutive integers with the sum of 42

Question

anonymous · Answer

@oldrin.bataku

anonymous · Answer

What is 42/3?

It's 14

Now you have to have numbers that are equal to 14(3)

13+14+15

This is very similar to the last question I showed you.
Is the concept sinking in?

anonymous · Answer

hmm

anonymous · Answer

so 14 is one of them..

texaschic101 · Answer

3 consecutive integers....that means one right after the other
Let x be the first integer, and let x + 1 be the second integer, and let x + 2 be the third integer.
x + x+ 1 + x + 2 = 42 -- combine like terms
3x + 3 = 42 -- subtract 3 from both sides
3x = 42 - 3
3x = 39 -- divide by 3
x = 13

anonymous · Answer

we're going to use the same method as before. let $n$ be our middle integer, so the first and third integers are $n-1$ and $n+1$ as a I mentioned before.

when we say the sum is $42$ we mean that if we add $n-1,n,n+1$ it should result in $42$ i.e.$$(n-1)+n+(n+1)=42\\dots$$

anonymous · Answer

solve for $n$ to determine the middle number. the first number will then be the one right before it ($n-1$) and the third will be the one right after it ($n+1$)

anonymous · Answer

Oh I see. oldrin has the right idea

Look at the formula two messages up. 14 is your "n"
Plug 14 into the formula and see if it works.
Remember you got 14 because 42/3 = 14

anonymous · Answer

so its 13 14 n 15

anonymous · Answer

but how would it be if it were to even integers

anonymous · Answer

Correct :)

anonymous · Answer

14 and 12 or 14 and 16

texaschic101 · Answer

it does not say even integers, it says consecutive integers

anonymous · Answer

Absolutely. As long as the the middle number is 14

The middle number of 13 and 15 is 15
The middle number of 12 and 16 is 14

anonymous · Answer

Sorry I mean The middle number of 13 and 15 is 14
And yes texaschic is correct. The question asks consecutively.

anonymous · Answer

if they asked for only even integers, then instead of using $n-1,n,n+1$ we would use $n-2,n,n+2$ -- the process is very similar. the only difference is that consecutive integers are only $1$ apart whereas even integers are $2$ apart

texaschic101 · Answer

or n , n + 2, and n + 4

anonymous · Answer

what about for 159

anonymous · Answer

52 53 and 54?

anonymous · Answer

@texaschic101 sure, if you pick $n$ to represent the first number -- but it's more natural to consider the middle number due to the symmetry of the problem. observe that when you sum $n,n+2,n+4$ you get $3n+6$ whereas summing $n-2,n,n+2$ gives just $3n$

anonymous · Answer

nvm it would be 79 and 80

texaschic101 · Answer

n + n + 1 + n + 2 = 159
3n + 3 = 159
3n = 159 - 3
3n = 156
n = 52

n + 1 = 53
n + 2 = 54