Suppose you have a friend named Ed. He and his four friends are having ice cream. There are only three flavors available at the ice cream store they are visiting: chocolate, vanilla, and strawberry. One of Ed’s friends, Stacey, eats chocolate exclusively. How many different kinds of cones can they make? They may have only singles, doubles, and triples. Create one or more number sentences that would support your conclusions.
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To determine the number of different kinds of cones they can make, we need to consider the different combinations of ice cream flavors and the number of scoops (singles, doubles, and triples) that can be chosen.
Since Stacey only eats chocolate, we can start by calculating the number of cone combinations excluding Stacey's choice.
For the remaining four friends, they have three flavor choices (vanilla, and strawberry, excluding chocolate) for each scoop. Since they can have singles, doubles, or triples, we have the following number of possibilities for each friend:
1 scoop: 3 choices (vanilla, and strawberry, excluding chocolate)
2 scoops: 3 choices for the first scoop, and 3 choices for the second scoop, giving us 3 * 3 = 9 possibilities
3 scoops: 3 choices for the first scoop, 3 choices for the second scoop, and 3 choices for the third scoop, giving us 3 * 3 * 3 = 27 possibilities
Now, let's consider Stacey's cone choice. She can only have the chocolate flavor, so for each of the remaining possibilities we calculated above, we need to add one cone with a single scoop of chocolate.
Therefore, the total number of different kinds of cones they can make is:
1 scoop: 3 choices (vanilla, and strawberry, excluding chocolate) + 1 choice (single scoop of chocolate) = 4 possibilities
2 scoops: 9 possibilities + 1 choice (single scoop of chocolate) = 10 possibilities
3 scoops: 27 possibilities + 1 choice (single scoop of chocolate) = 28 possibilities
To summarize:
- Cones with 1 scoop: 4 possibilities
- Cones with 2 scoops: 10 possibilities
- Cones with 3 scoops: 28 possibilities
Therefore, they can make a total of 4 + 10 + 28 = 42 different kinds of cones.
Number sentences supporting the conclusions:
1. Number of cones with 1 scoop = 3 flavors (excluding chocolate) + 1 choice (chocolate) = 4 possibilities.
2. Number of cones with 2 scoops = 9 possibilities (excluding chocolate) + 1 choice (chocolate) = 10 possibilities.
3. Number of cones with 3 scoops = 27 possibilities (excluding chocolate) + 1 choice (chocolate) = 28 possibilities.
Adding the above numbers to find the total: 4 + 10 + 28 = 42 different kinds of cones.