SOLUTION: It's been a longtime and I don't remember none of this stuff. Your help would be greatly appreciated. My problem is: The product of the page numbers on two facing pages of a b

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: It's been a longtime and I don't remember none of this stuff. Your help would be greatly appreciated. My problem is: The product of the page numbers on two facing pages of a b      Log On


   

Question 185351: It's been a longtime and I don't remember none of this stuff. Your help would be greatly appreciated.
My problem is:
The product of the page numbers on two facing pages of a book is 132. Find the page number? There are n teams in a league and the number of games played is given by the polynomial n2 -n =N. A woman softball leagues has 11 teams. what is the total numbers of games to be played?

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Question #1: "The product of the page numbers on two facing pages of a book is 132. Find the page number?"


Note: consecutive numbers are of the form x, x+1, x+2, etc...


So "The product of the page numbers on two facing pages of a book is 132" translates to x%28x%2B1%29=132


x%28x%2B1%29=132 Start with the given equation


x%5E2%2Bx=132 Distribute


x%5E2%2Bx-132=0 Subtract 132 from both sides.


%28x%2B12%29%28x-11%29=0 Factor the left side


x%2B12=0 or x-11=0 Use the zero product property to break up the equation


x=-12 or x=11 Solve for "x"


Now ignoring the negative solution x=-12 (you can't have a negative page number), this means that the only answer is x=11


So the page numbers are 11 and 12


Note: 11*12=132


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Question #2: "There are n teams in a league and the number of games played is given by the polynomial n2 -n =N. A woman softball leagues has 11 teams. what is the total numbers of games to be played? "



Note: since "n" is the number of teams and there are 11 softball teams, this means that in this case n=11


n%5E2-n=N Start with the given equation


11%5E2-11=N Plug in n=11 (see above)


121-11=N Square 11 to get 11*11=121


110=N Subtract


So there are 110 games played.