Ashley puts 45 stamps in an album. She puts the same number of stamps on each page, and 3 stamps on the last page. There are 2 more pages in the album than the number of stamps on each page. How many pages are in the album? How many stamps are on each page?

45 pages total

3 on last page

45-3=42

there are 42 on the rest of the pages

on each page, there are 2 more pages in album than then stamps on pages

amount of stamps on pages with equal number of stamps is

A=numberofpgest times number of stamps on pages

number of pages=p

number of stamps per papge=s

a=ps

2 more pages than stamps on pages

p=2+s

total number of stamps per page is s = (45-3) / (p-1)

(what I did is I first got rid of number of stamps on last page, then got rid of the last page)

P=2+s

s = (45-3) / (2+s-1)

s=42 / (s+1)

times s+1 both sides

s^2+s=42

minus 42

s^2+s-42=0

factor

(s-6) (s+7) = 0

set equal to zero

s-6=0

s=6

s+7=0

s=-7, false, no negative stamps

6 stamps per page

sub

p=2+s

p=2+6

p=8

8 pages

check

last page is 3 so 8-1=7 page left

7*6=42

3+42=45

correct

there are

8 pages in the album

6 stamps per page