SOLUTION: Find three consecutive odd integers such that the product of the smaller two is 15 more than four times the sum of the three integers?

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: Find three consecutive odd integers such that the product of the smaller two is 15 more than four times the sum of the three integers?      Log On


   

Question 963811: Find three consecutive odd integers such that the product of the smaller two is 15 more than four times the sum of the three integers?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
N=smallest integer; N+2=middle integer; N+4=largest integer
%28N%29%28N%2B2%29=4%28N%2BN%2B2%2BN%2B4%29%2B15
N%5E2%2B2N=4%283N%2B6%29%2B15
N%5E2%2B2N=12N%2B24%2B15 Subtract 12N from each side.
N%5E2-10N=39 Subtract 39 from each side.
N%5E2-10N-39=0
%28N-13%29%28N%2B3%29=0
N-13=0 or N%2B3=0
N=13 or N=-3
ANSWER 1: The smallest integer is 13.
N+2=13+2=15 ANSWER 2: The middle integer is 15.
N+4=13+4=17 ANSWER 3: The largest integer is 17.
CHECK:
%28N%29%28N%2B2%29=4%28N%2BN%2B2%2BN%2B4%29%2B15
%2813%29%2815%29=4%2813%2B15%2B17%29%2B15
195=4%2845%29%2B15
195=180%2B15
195=195