Cookies are sold singly or in packages of 2 or 6. with this packaging, how many ways can you buy exactly 10 cookies? Please help immediately!!!
6+1+1+1+1 = 10
6+2+2 = 10
you can replace each 2 with two 1's
or you can replace the 6 with three more 2's.
To find the number of ways you can buy exactly 10 cookies, you can break it down into cases:
Case 1: Buying 10 individual cookies
Since cookies are sold singly, you can buy 10 individual cookies.
Case 2: Buying 5 packages of 2 cookies
In this case, you buy 5 packages of 2 cookies each, which will give you a total of 10 cookies.
Case 3: Buying 1 package of 6 cookies and 2 individual cookies
In this case, you buy 1 package of 6 cookies and 2 individual cookies, which will also give you a total of 10 cookies.
Therefore, there are 3 ways you can buy exactly 10 cookies:
1) Buying 10 individual cookies.
2) Buying 5 packages of 2 cookies each.
3) Buying 1 package of 6 cookies and 2 individual cookies.
I hope this helps!
To find the number of ways to buy exactly 10 cookies, we can use the concept of combinations. We will consider the number of cookies bought as the number of items selected from a set.
Let's break down the problem into cases:
1. Buying only single cookies: In this case, we need to find a combination of 10 single cookies. However, since the cookies are sold singly, we can buy only 1 cookie at a time. So there is only one way to buy exactly 10 single cookies.
2. Buying cookies in packages of 2: In this case, we need to find a combination of 2 cookies that sums to 10. Let's list down the possible combinations:
- (2, 2, 2, 2, 2): 5 packages of 2 cookies.
- (6, 2, 2): 1 package of 6 cookies, and 2 packages of 2 cookies.
- (2, 6, 2): 1 package of 6 cookies, and 2 packages of 2 cookies.
- (2, 2, 6): 1 package of 6 cookies, and 2 packages of 2 cookies.
- (6, 4): 1 package of 6 cookies, and 1 package of 2 cookies.
- (4, 6): 1 package of 6 cookies, and 1 package of 2 cookies.
- (8, 2): 1 package of 6 cookies, and 1 package of 2 cookies.
- (2, 8): 1 package of 6 cookies, and 1 package of 2 cookies.
So there are 8 different ways to buy exactly 10 cookies using packages of 2.
3. Buying cookies in packages of 6: In this case, we need to find a combination of 6 cookies that sums to 10. However, there is no possible combination since the highest multiple of 6 less than 10 is 6 itself, which leaves a remainder of 4.
Therefore, there is only one way to buy exactly 10 cookies using only single cookies and 8 ways to buy exactly 10 cookies using packages of 2, resulting in a total of 9 ways to buy 10 cookies.