SOLUTION: I need help with an algebra 2 question. The question is: "Find three positive consecutive integers such that the product of the smallest and largest is 17 more than three times th

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Question 1124936: I need help with an algebra 2 question. The question is:
"Find three positive consecutive integers such that the product of the smallest and largest is 17 more than three times the median integer."

Found 3 solutions by josgarithmetic, greenestamps, MathLover1:
Answer by josgarithmetic(39626)   (Show Source):
You can put this solution on YOUR website!
"Find three positive consecutive integers such that the product of the smallest and largest is 17 more than three times the median integer."

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and

------solve this.
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The value which works here is .

The numbers for the solution are 5, 6, 7.

Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!

This problem is a good example of how, in a problem involving three consecutive integers, it is often much easier to solve if you let your variable represent the middle integer. So....

Let the three integers be x-1, x, and x+1.

The problem says the product of the smallest and largest is 17 more than 3 times the middle number:

Expanding and simplifying will give you a quadratic equation that is easily solved by factoring.

Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!

let three positive consecutive integers be , , and

...factor

solutions:
if ->
if ->
since you need three consecutive integers, use
and three numbers are:

check: