SOLUTION: The product of 2 consecutive odd numbers is 63. What is the larger number?

Question 245881: The product of 2 consecutive odd numbers is 63. What is the larger number?
Found 3 solutions by College Student, unlockmath, Alan3354:
Answer by College Student(505)   (Show Source): You can put this solution on YOUR website!
Let x = a number
Let x+2 = its consecutive odd number
.
Since the product of two consecutive odd numbers is 63, the equation becomes:

.
Let's work out the algebra.

Factor:

.
In order to make our above equation true, the solution set is x = {7,-9}.
Let's check which one works for our problem:
.

<--- 7 works!
So, x=7 and x+2=9.
.

<--- -9 also works!
So, x=-9 and x+2=-7.
.
Both solution sets fit our criteria.
Both are odd numbers and both are odd consecutives which product is 63.
Answer by unlockmath(1688)   (Show Source): You can put this solution on YOUR website!
Hello,
The way to do this is first let x be an odd number and the next odd number would be x+2. Make sense? Now we can set up an equation like this:
x(x+2)=63 Distribute this so it looks like:
x^2+2x=63 Subtract 63 from both sides gives us:
x^2+2x-63 This can be factored into:
(x+9)(x-7)=0 Solve x will be:
x=-9
x=7
From the two answers only 7 makes sense, so the larger number would be 9.
The above is how to solve it using algebra.
There is a faster way to figure it out by just thinking what two numbers multiplied together gives us 63. Of course the answer is 7 and 9
RJ Toftness
Check out my book at www.math-unlock.com
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
The sqrt(63) is almost 8.
The 2 odd numbers are adjacent to 8, = 7 and 9.
Also, -7 and -9.
--------------
Always use the easiest and quickest method.
It saves time, which is important on tests, and there's less chance of making an error.

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