The sum of two consecutive even integers is 234. What is the larger integer?

114
116
118
124

Question

The sum of two consecutive even integers is 234. What is the larger integer?

 114
 116
 118
 124

zzr0ck3r · Answer

take some number $n$ then the next one is $n+1$ so we have $n+n+1=234$ solve for $n$ and then the bogger one is $n+1$

robtobey2 · Answer

116 + 118 = 234

whpalmer4 · Answer

@zzr0ck3r but the problem says the sum of two consecutive EVEN integers...

torialaw192 · Answer

@whpalmer4 That's where I'm lost at.

whpalmer4 · Answer

and $$2n+1 = 234$$has no integer solutions...

whpalmer4 · Answer

okay, if we have a number, and it is even, let's call it $n$.  what is the value of the next even number?

whpalmer4 · Answer

$2$ is even.  what's the next even number after $2$?

robtobey2 · Answer

n + n - 2 = 234 // Solve
m = 118

torialaw192 · Answer

4.

wolf1728 · Answer

2N + (2N +2) = 234

robtobey2 · Answer

n = 118
sorry.

whpalmer4 · Answer

right.  if we start with an even number, the next even number is 2 greater.

so our first number is $n$ and our second is $n+2$ and the two of them add to $234$

$$n+(n+2) = 234$$$n$ is the smaller number, and $n+2$ is the larger.  easy algebra to find the values...

wolf1728 · Answer

seems rob got the equation right before I did.

wolf1728 · Answer

Geez there's EIGHT people working on this??

zzr0ck3r · Answer

woops
2n and 2n+2 so 2n+2n+2=234

4n=232

n=58

So our numbers are 2*58 and 2*58+1

torialaw192 · Answer

But I'm still confused on how to work it out.

zzr0ck3r · Answer

I just worked it out, which part are you confused about?

whpalmer4 · Answer

$$n+(n+2) = 234$$
$$n+n+2 = 234$$$$n+n + 2 -2 = 234 - 2$$$$2n = 232$$$$\frac{2n}{2} = \frac{232}{2}$$$$n=116$$
$$n+2=116+2=118$$

$$116+118=234\checkmark$$

torialaw192 · Answer

Pretty much on all the parts.

whpalmer4 · Answer

@zzr0ck3r is writing the problem in a way that doesn't require you to assume that you have an even number, at the cost of making it perhaps more confusing.  My way, I just assume that the numbers that pop out at the end are even, and verify that they are.

torialaw192 · Answer

@zzr0ck3r

Oh.

whpalmer4 · Answer

Another way you could come up with the answer is to realize that if you have two consecutive numbers (or consecutive even numbers, in this case) which add up to some other number, those numbers must be just about half of the number they add up to, right?  234/2 = 117, but that is odd, not even, so your numbers must the be the consecutive even numbers which straddle 117, namely 116 and 118.

torialaw192 · Answer

@whpalmer4 Ok.

whpalmer4 · Answer

Any way you work the problem, be sure to check your answer to make sure that it makes a true statement when plugged into the problem.  116 and 118 are both even, check.  There aren't any even numbers between them (which would mean they were not consecutive), check.  The two of them added together give you 234, check.  Now all that is left is writing down the correct answer, which is the larger of the two...

torialaw192 · Answer

118

whpalmer4 · Answer

There you go!

torialaw192 · Answer

@whpalmer4 Thank you.