SOLUTION: The product of two consecutive positive even integers is 360. Find the integers.

Question 113275: The product of two consecutive positive even integers is 360. Find the integers.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Consecutive even integers follow the form: , , etc

So when they say "The product of two consecutive positive even integers is 360", they mean symbolically:

Distribute

Subtract 360 from both sides

Factor

Factor (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:

or

or Now solve for x in each case

So our solutions are or

However, since it is stated that the integers must be positive, is the only solution

Now plug into to find the 1st number:

So our 1st number is 18

Now plug into to find the 2nd number:

So our 2nd number is 20

So our two numbers are 18 and 20

Check:

When we multiply 18 and 20, we should get 360

Since we do, our answer is verified.
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