Question

Please answer with some work shown!

- Kirstin is decorating her bedroom wall with photographs.
She has 36 photographs of family and 28 photographs of friends.
She wants to arrange the photographs in rows so that each row
has the same number of photographs, and photographs of family
and photographs of friends do not appear in the same row.
a. How many rows will there be if Kirstin puts the greatest possible
number of photographs in each row?

b. How many photographs will be in each row?

Answer 1

Kirstin can arrange her photographs in a total of 16 rows, with 4 photographs per row. This arrangement uses the greatest common divisor of the number of family and friend photographs she has.

Step-by-step explanation:

To find out how Kirstin can arrange her photographs, we need to look for the greatest common divisor (GCD) of the number of family photographs and friend photographs, since she wants the same number of photographs in each row and wants to have separate rows for family and friends. The GCD of 36 (family photographs) and 28 (friend photographs) is 4. This tells us the greatest number of photographs we can have in each row while being able to divide both sets of photographs evenly into rows.

Now let's calculate the total number of rows:

• For family photographs: 36 photographs ÷ 4 photographs per row = 9 rows
• For friend photographs: 28 photographs ÷ 4 photographs per row = 7 rows

Therefore, Kirstin will need a total of 16 rows to arrange all her photographs (9 rows of family and 7 rows of friends).

As for the number of photographs in each row, she can fit 4 photographs per row which is the greatest common divisor we found earlier.

Answer 2

there will be 8 rows

the number of photographs in each row is 8