SOLUTION: Two consecutive numbers have a sum of 35 and a product of 306. Find the smaller number.
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Question 906256: Two consecutive numbers have a sum of 35 and a product of 306. Find the smaller number.
Found 2 solutions by Theo, nihar*2013:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x is the first number
x+1 is the second number.
you get:
x + x + 1 = 35
x * (x+1) = 306
simplify to get:
2x+1 = 35
x^2+x = 306
from the first equation, solve for x to get x = 17.
it looks like one of your numbers has to be 17.
then the other number must be 18 because the numbers are consecutive starting from 17.
multiply 17 * 18 and you get 306 so this confirms that the numbers are 17 and 18.
if you had solved for x in the second eqaution, it would have given you x = 17 as well.
x^2 + x = 306 is the second equation.
subtract 306 from both sides of the equation to get x^2 + x - 306 = 0
factor the equation to get (x+18) * (x-17) = 306
solve for x to get x = -18 or x = 17
x can't be -18 because -18 * -17 results in -306 and not 306.
therefore x has to be 17.
17*18 = 306
17+18 = 35
since you are asked to find the smaller number, then your solution is that the smaller number is equal to 17.
Answer by nihar*2013(34) (Show Source): You can put this solution on YOUR website!
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