Question 185351
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(x+1)=132}}}



{{{x(x+1)=132}}} Start with the given equation



{{{x^2+x=132}}} Distribute



{{{x^2+x-132=0}}} Subtract 132 from both sides.



{{{(x+12)(x-11)=0}}} Factor the left side



{{{x+12=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^2-n=N}}} Start with the given equation



{{{11^2-11=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.