SOLUTION: what are three consecutive odd numbers whose sum is 105?

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Question 96237: what are three consecutive odd numbers whose sum is 105?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since 2x refers to any even number, 2x%2B1 refers to any odd number. So the sum of three consecutive odd numbers is:

%282x%2B1%29%2B%282x%2B3%29%2B%282x%2B5%29



%282x%2B1%29%2B%282x%2B3%29%2B%282x%2B5%29=105 Start with the translated equation



%282x%2B2x%2B2x%29%2B%281%2B3%2B5%29=105 Group like terms on the left side

6x%2B9=105 Combine like terms on the left side


6x=105-9Subtract 9 from both sides


6x=96 Combine like terms on the right side


x=%2896%29%2F%286%29 Divide both sides by 6 to isolate x



x=16 Reduce



Now plug in x=16 into 2x%2B1


2%2816%29%2B1=32%2B1=33


So the first number is 33

Now plug in x=16 into 2x%2B3

Second Number:

2%2816%29%2B3=32%2B3=35

Now plug in x=16 into 2x%2B5
Third Number:

2%2816%29%2B5=32%2B5=37

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Answer:

So the three numbers are 33,35, and 37