The product of two consecutive integers is 306. Find the integers.
The hardest part is understanding what the question is asking and setting up the problem. Once you have this, it is a piece of cake. Here's what we do:
First what its asking: (Break the question down into segments)
The product: Ok this means Multiply.
Two consecutive integers:
This means that the second number comes right after the first number in a number line. Ex. 1,2,3,4,5...
The integers belong to the number 306:
Factor 306.
306
^
2*153
^
9*17
^
3*3
Now look 3 * 3 * 2 = 18
The other factor 306 = 17
These two are consecutive numbers so these are your integers since 18 * 17 = 306.
A more Algebraic approach would be to say:
two consecutive intergers are multiplied together to make 306
x(x + 1) = 306
x^2 + x = 306
x^2 + x - 306 = 0
(x - 17)(x+18) = 0
x - 17 = 0; x = 17
x - 18 = 0; x = 18
There are your two consecutive integers.