Question

Cookies are sold singly or in packages of

66


or


1818.


With this​ packaging, how many ways can you buy


3636


​cookies

Answer 1

only 2 packages of 1818 cookies

Explanation:

If I want to buy only big packages

`3636 / 1818 = 2`

Then, i can buy exactly 3636 cookies buying 2 packages of 1818 cookies.

If i want to buy only mall packages

`3636 / 66 = 55.09`

Then, there is no way to buy only small packages and get exactly 3636 cookies.

(with 55 packages i get 55x66=3630 and with 56 packages 56x66=3696)

If i want to buy a combination of both packages i can only buy one big package and the rest in small packages.

`3636 - 1818 = 1818 \\ 1818 / 66 = 27.55`

Then, there is no way to buy one big and the rest small packages and get exactly 3636 cookies.

(with one big package and 27 small packages we get 1818+27x66=3600 and with one big package and 28 small 1818+28x66=3666)

Then, the only way to get 3636 cookies is with two packages of 1818.