SOLUTION: There are three consecutive odd integers. The middle integer is 116 less than three times the smallest integer. What are the three integers?

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Question 216857: There are three consecutive odd integers. The middle integer is 116 less than three times the smallest integer. What are the three integers?
Answer by drj(1380) About Me  (Show Source):
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There are three consecutive odd integers. The middle integer is 116 less than three times the smallest integer. What are the three integers?

Step 1. Let n be the smallest odd integer.

Step 2. Let n+2 and n+4 be the next two odd and consecutive integers.

Step 3. Let 3n be three times the smallest integer

Step 4. Then n+2=3n+116 since middle integer is 116 less than three times the smallest integer

Step 5. Solving the equation in Step 4 yields the following steps

n%2B2=3n-116

Add 116-n to both sides of the equation

n%2B2%2B116-n=3n-116%2B116-n

118=2n

Divide 2 to both sides of the equation

118%2F2=2n%2F2

59=n

Then n%2B2=61 and n%2B4=63

Check middle integer....61=3*59-116=61...which is a true statement.

Step 6. ANSWER: The integers are 59, 61, and 63.

I hope the above steps were helpful.

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And good luck in your studies!

Respectfully,
Dr J