SOLUTION: A student opens a mathematics book to two facing pages. The product of the page numbers is 2352. Find the page numbers. The first page is? and The second page is?

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A student opens a mathematics book to two facing pages. The product of the page numbers is 2352. Find the page numbers. The first page is? and The second page is?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 328726: A student opens a mathematics book to two facing pages. The product of the page numbers is 2352. Find the page numbers. The first page is? and The second page is?
Found 2 solutions by checkley77, josmiceli:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
X(X+1)=2352
X^2+X-2352=0
(X+49)(X-48)=0
X-48=0
X=48 IS THE NUMBER OF THE LEFT HAND PAGE.
48+1=49 IS THE NUMBER OF THE RIGHT HAND PAGE. pROOF:
48*49=2352
2352=2352

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the first page p
The 2nd page will be p%2B1
given:
p%2A%28p%2B1%29+=+2352
p%5E2+%2B+p+=+2352
Complete the square:
p%5E2+%2B+p+%2B+%281%2F2%29%5E2+=+2352+%2B+%281%2F2%29%5E2
%28p+%2B+1%2F2%29%5E2+=+2352+%2B+1%2F4
%28p+%2B+1%2F2%29%5E2+=+9409%2F4
Take the square root of both sides
p+%2B+1%2F2+=+97%2F2
p+=+97%2F2+-+1%2F2
p+=+96%2F2
p+=+48
p+%2B+1+=+49
The pages are 48 and 49
check:
48%2A49+=+2352
OK