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- anonymous

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

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- anonymous

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

- mathstudent55

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

- mathstudent55

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

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- anonymous

224/2 made it easier

- mathstudent55

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

112

- anonymous

but thats not answer

- anonymous

wait would it be 110 and 112?

- mathstudent55

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

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

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

- anonymous

nope...

- mathstudent55

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

- anonymous

its 226 not 228

- anonymous

i got 114

- mathstudent55

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

226/2 is not 114

- mathstudent55

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

- anonymous

wait the answer is 114!?

- mathstudent55

Yes.

- freckles

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

- freckles

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

- anonymous

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

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