Final answer:
There are three ways to buy 66 cookies with packaging options of single cookies, or packages of 11 or 33. They are two packages of 33, six packages of 11, or sixty-six single cookies.
Step-by-step explanation:
To find out how many ways you can buy 66 cookies using single cookies, or packages of 11 or 33, we can set up a problem using combinations of these quantities. As we know, 66 is a multiple of both 11 and 33, so we'll want to find out how many packages of 11 and how many packages of 33 can be combined without exceeding 66.
Firstly, since 33 is exactly half of 66, we can have either two packages of 33 or zero packages of 33. If we choose two packages of 33, then we have no need for additional cookies. If we choose zero packages of 33, we can then use six packages of 11 to make up the total because 6 x 11 = 66. There's also the option of buying 66 single cookies, although that tends to be inefficient.
So, our possibilities are:
- Two packages of 33 cookies
- Six packages of 11 cookies
- Sixty-six single cookies
Thus, there are three ways to buy 66 cookies given the packaging constraints.