Question

At a scrapbooking party, guests brought a certain number of photographs to use, based on

how many pages they will be assembling. Ellie plans to assemble 4 small pages and 7 large
pages and brought a total of 22 photographs to use. Bridgette brought 30 photographs,
which is enough to assemble 8 small pages and 7 large pages. Assuming that the number of
photographs on a page remains constant, how many photographs fit on a small page and a
large page?
A small page can fit
photographs, and a large one can fit
photographs.

Answer 1

A small page can fit 2 photographs, and a large on can fit 2 photographs.

Explanation:

Let the number of photographs on the small page be represented by m and that of large one by n.

Since the number of photographs on a page remains constant, then;

4m + 7n = 22 ........... 1

8m + 7n = 30 .......... 2

Multiply equation 1 by 2, and 2 by 1 to have;

8m + 14n = 44 ....... 3

8m + 7n = 30 ......... 4

subtract equation 4 from 3,

7n = 14

n = 2

Substitute the value of n in equation 1

4m + 7(2) = 22

4m + 14 = 22

4m = 8

m = 2

m = 2, n = 2

Therefore, a small page can fit 2 photographs, and a large on can fit 2 photographs so that the number of photographs n a page is constant.