anonymous
  • 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
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
x + x + 2 = 226 Or, 2x = 224 Now can you solve it for x
mathstudent55
  • mathstudent55
We can solve this with an equation. We start by choosing a variable. Let x be the smaller number.
mathstudent55
  • mathstudent55
The next larger even number is 2 larger than x, that makes the larger number x + 2.

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anonymous
  • anonymous
224/2 made it easier
mathstudent55
  • 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
  • anonymous
112
anonymous
  • anonymous
but thats not answer
anonymous
  • anonymous
wait would it be 110 and 112?
mathstudent55
  • 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
  • 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
  • anonymous
would it be 110 and 112? no.. 110 and 108???
anonymous
  • anonymous
nope...
mathstudent55
  • mathstudent55
110 + 112 = 222 110 + 108 = 218 Neither of the above add to 226, so they cannot be correct.
anonymous
  • anonymous
its 226 not 228
anonymous
  • anonymous
i got 114
mathstudent55
  • 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
  • anonymous
226/2 is not 114
mathstudent55
  • mathstudent55
Follow my responses above to understand how to get the answer.
anonymous
  • anonymous
wait the answer is 114!?
mathstudent55
  • mathstudent55
Yes.
freckles
  • freckles
yes they were saying x+2>x for positive number x
freckles
  • freckles
and you found the x so you could plug that x into x+2 to find the large of the two
anonymous
  • anonymous
lol yeah ???? i did not know how to explain it

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