the product of two consecutive numbers is 10 more than the square of the smaller number.

Question

anonymous · Answer

find the smaller number

anonymous · Answer

Numbers are x and x+1.
x(x+1) = 10 + x^2.
Solve for x.

agreene · Answer

$$n*(n+1)=10+ n^2$$

anonymous · Answer

how did you guys know to write the equation out like that.

agreene · Answer

well, it says product so we know we are multiplying. the numbers are consecutive, which means they are one after another in the number line, so one must be x and the other x+1. we know this product is equal to 10 more (addition) than the smaller (first number) squared.

anonymous · Answer

It is confusingly worded, but if you read it carefully you can translate it into a equation.  Usually you have to look for the thing that's unknown and assign it a letter.  Then look at how it's related to other quantities they give you and express that in math.

It started by saying "the product of two consecutive numbers."  We don't know what they are, but if we call one x then the other one is x+1.  (It could also be x-1 and we'd get the same answer, but I like + better.)  The product is x(x+1).  That's all we have so far.

Then it said "is."  That means equal.  We have one quantity, x(x+1).  That's gonna go on one side of the equal sign.  But what's on the other?  Don't know yet; let's keep reading.

"10 more than."  So something plus 10.  Same thing as 10 plus something, so 10+... don't know yet.

"the square of the smaller number" Which is smaller, x or x+1?  Always x.  So x^2.

Put all the steps together and we get
x(x+1) = 10 + x^2

Now reread the question and make sure the equation looks right, and see if you missed any other information.  If everything's okay, then we just have a simple equation that we know how to solve.  So solve it.