SOLUTION: Please help solve I am very confused with this problem. A student opens a book to 2 facing pages. The product of the page number is 1056. Find the page numbers. 1st page is 2

Algebra ->  Equations -> SOLUTION: Please help solve I am very confused with this problem. A student opens a book to 2 facing pages. The product of the page number is 1056. Find the page numbers. 1st page is 2      Log On


   

Question 132301: Please help solve I am very confused with this problem.
A student opens a book to 2 facing pages. The product of the page number is 1056. Find the page numbers.
1st page is
2nd page is
Thanks.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If we look at the page numbers, we'll notice that they are consecutive integers. So they follow the algebraic form x, x%2B1, x%2B2, etc.



So if the product of two consecutive integers is 1056, then we have the equation

x%28x%2B1%29=1056


x%5E2%2Bx=1056 Distribute


x%5E2%2Bx-1056=0 Subtract 1,056 from both sides

%28x%2B33%29%28x-32%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x%2B33=0 or x-32=0

x=-33 or x=32 Now solve for x in each case


So our possible solutions are

x=-33 or x=32



However, since a negative page number is not possible, this means that the only solution is x=32


Now to find the next page number, simply add 1 to 32 to get


32%2B1=33


So the two page numbers are 32 and 33



Check:

To check this answer, simply multiply the two numbers:


32%2A33=1056


1056=1056 Works.