SOLUTION: Three consecutive even integers are such that the product of the first two is 6 less than 9 times the third. Find the integers.

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: Three consecutive even integers are such that the product of the first two is 6 less than 9 times the third. Find the integers.      Log On


   

Question 119683: Three consecutive even integers are such that the product of the first two is 6 less than 9 times the third. Find the integers.
Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
Put the given words into an equation. Let x be the first even integer. Then x+2 is the next even integer (since you need to add 2 to a given even number to get the next even number), and x+4 is the next even integer:
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x%28x%2B2%29=9%28x%2B4%29-6
Multiply through:
x%5E2%2B2x=9x%2B36-6
Put the quadratic into standard form:
x%5E2-7x-30=0
Factor:
%28x%2B3%29%28x-10%29=0
Solve for x:
x%2B3=0
x=-3
Note that this value for x is no good for this problem, since it is an odd number.
x-10=0
highlight%28x=10%29
Remember, x is the first even integer. So the three even integers are:
10,12,14
You can verify this result to see if the given holds true with these numbers.
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Good Luck,
tutor_paul@yahoo.com