Question

Cookies are sold singly or in packages of 6 or 18. With this​ packaging, how many ways can you buy 36 ​cookies?

Answer 1

█ Explanation █

The different ways I could buy the cookies include ...

✦ 2 eighteen packs 
✦ 3 six packs and 1 eighteen pack
✦ 1 eighteen pack and 18 singles
✦ 6 six packs
✦ 1 six pack, 1 eighteen pack and 12 singles
✦ 36 singles
✦ 5 six packs and 6 singles
✦ 4 six packs and 12 singles
✦ 3 six packs and 18 singles
✦ 2 six packs and 24 singles
✦ 1 six pack and 30 singles

That's a total of 11 ways.

Hope that helps! ★ If you have further questions about this question or need more help, feel free to comment below or leave me a PM. -UnicornFudge aka Nadia

Answer 2

Answer with Step-by-step explanation:

We know that 6×6=36 and 18×2=36

i.e. 6 pack cookies cannot exceed 6 and 18 pack cookies cannot exceed 2 in order to buy 36 cookies.

Now making combinations:

Buying 6 6 cookie pack and 0 18 cookie pack and 0 single cookies

Buying 5 6 cookie pack and 0 18 cookie pack and 6 single cookies

Buying 4 6 cookie pack and 0 18 cookie pack and  12 single cookies

Buying 3 6 cookie pack and 1 18 cookie pack and 0 single cookies

Buying 3 6 cookie pack and 0 18 cookie pack and 18 single cookies

Buying 2 6 cookie pack and 0 18 cookie pack and 24 single cookies

Buying 2 6 cookie pack and 1 18 cookie pack and 6 single cookies

Buying 1 6 cookie pack and 0 18 cookie pack and 30 single cookies

Buying 1 6 cookie pack and 1 18 cookie pack and 12 single cookies

Buying 0 6 cookie pack and 0 18 cookie pack and 36 single cookies

Buying 0 6 cookie pack and 1 18 cookie pack and 18 single cookies

Buying 0 6 cookie pack and 2 18 cookie pack and 0 single cookies

Hence, the total number of ways we can buy 36 cookies is:

12