PLEASE HELP I WILL MEDAL AND FAN
The sum of two consecutive even integers is 226. What is the larger integer?

114
116
112
118

Question

PLEASE HELP I WILL MEDAL AND FAN
The sum of two consecutive even integers is 226. What is the larger integer?

 114
 116
 112
 118

anonymous · Answer

x + x + 2 = 226

Or,

2x = 224

Now can you solve it for x

mathstudent55 · Answer

We can solve this with an equation.
We start by choosing a variable.
Let x be the smaller number.

mathstudent55 · Answer

The next larger even number is 2 larger than x, that makes the larger number x + 2.

anonymous · Answer

224/2 made it easier

mathstudent55 · Answer

Since we are told what the sum of the two consecutive even numbers is, we use our expressions with x and we follow what the problem tells us.
The sum of the two consecutive even numbers is x + x + 2.
We are told the sum is equal to 226, so that gives us our equation:

$x + x + 2 = 226$

anonymous · Answer

112

anonymous · Answer

but thats not answer

anonymous · Answer

wait would it be 110 and 112?

mathstudent55 · Answer

Now we add the like terms on the left side:

$2x + 2 = 226$

We subtract 2 from both sides:

$2x = 224$

The next step is to divide both sides by 2:

$x = 112$

Now we need to go back to our use of the variable x.

mathstudent55 · Answer

We said above that x is the SMALLER of the two numbers.
The problem is asking for the larger of the two numbers.
The larger number is x + 2, so 112 + 2 = 114.

The answer is: the larger number is 114.

anonymous · Answer

would it be 110 and 112? no.. 110 and 108???

anonymous · Answer

nope...

mathstudent55 · Answer

110 + 112 = 222
110 + 108 = 218
Neither of the above add to 226, so they cannot be correct.

anonymous · Answer

its 226 not 228

anonymous · Answer

i got 114

mathstudent55 · Answer

Just because you solved the equation for x, it does not mean you have finished.
You need to see what x represents and make sure you answer the question that is being asked.

anonymous · Answer

226/2 is not 114

mathstudent55 · Answer

Follow my responses above to understand how to get the answer.

anonymous · Answer

wait the answer is 114!?

mathstudent55 · Answer

Yes.

freckles · Answer

yes they were saying x+2>x for positive number x

freckles · Answer

and you found the x 
so you could plug that x into x+2 to find the large of the two

anonymous · Answer

lol yeah ???? i did not know how to explain it