SOLUTION: What three consecutive numbers have a sum that is 1/5 of their product?

Question 226398: What three consecutive numbers have a sum that is 1/5 of their product?
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
What three consecutive numbers have a sum that is 1/5 of their product?

Step 1. Let be one number.

Step 2. Let and be the next two consecutive numbers.

Step 3. Let be the sum

Step 4. Let be of their product

Step 5. Then, since the three consecutive numbers have a sum that is 1/5 of their product.

Step 6. Solving equation in Step 5, yields the following steps.

Divide to simplify equation

Multiply by 5 to get rid of denominator

Subtract 15 from both sides of the equation

Step 7. Factoring the above quadratic equation yields the following

Step 8. So and or and

Step 9. With , and . Check these numbers with the equation in Step 5 . And

which is a true statement

Step 10. With , and . Check these numbers with the equation in Step 5 . And

which is a true statement.

Step 11. ANSWER: There are two sets of consecutive numbers, they are 3, 4, 5 and -5, -4, -3.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J

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