SOLUTION: Find three consecutive odd intergers such that the sum of all three is 36 less than the product of the smaller two. Show the equation and all the steps.

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: Find three consecutive odd intergers such that the sum of all three is 36 less than the product of the smaller two. Show the equation and all the steps.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 530521: Find three consecutive odd intergers such that the sum of all three is 36 less than the product of the smaller two. Show the equation and all the steps.
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
Three consecutive odd integers can be defined as:
x
x+2
x+4
.
The sum of these three number is 36 less than the product of the smaller two.
.
x +x+2 +x+4 +36 = x*(x+2)
.
Solve
.
3x + 42 = x^2 + 2x
.
x^2 -x -42 = 0
.
Factor
.
(x-7)(x+6) = 0
.
x = 7 or -6
.
-6 is not odd, so we select 7 as the answer.
.
x = 7
x+2 = 9
x+4 = 11
.
Check the values.
7*9 = 63
7+9+11 = 27
27+36 = 63
Correct
.
Answer: The numbers are 7, 9, and 11.
.
Done.