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. Post your solution as a response to this thread.
Please type your subject in the School Subject box. Any other words, including obscure abbreviations, are likely to delay responses from a teacher who knows that subject well.
To find the number of different kinds of cones they can make, we need to consider the number of people and the number of flavors available.
Let's analyze the given information step by step:
1. Number of flavors available: There are three flavors available - chocolate, vanilla, and strawberry.
2. Ed's friend, Stacey: Stacey eats chocolate exclusively, which means that she can only have the chocolate flavor.
Now, let's consider the different possibilities for Ed and his other three friends:
For each cone, Ed and his friends can choose one, two, or three flavors.
Case 1: Single cones
In this case, each person chooses only one flavor for their cone.
Ed has 3 choices (chocolate, vanilla, or strawberry).
His four friends (excluding Stacey) have 2 choices each (vanilla or strawberry) since Stacey already has chocolate.
So, the number of single cones they can make is:
Ed: 3 choices
Friend 1: 2 choices
Friend 2: 2 choices
Friend 3: 2 choices
Friend 4: 2 choices
Total number of single cones = 3 * 2 * 2 * 2 * 2 = 48 cones
Case 2: Double cones
In this case, each person can choose two flavors for their cone.
Ed has 3 choices (chocolate, vanilla, or strawberry).
His four friends (excluding Stacey) have 2 choices each (vanilla or strawberry) since Stacey already has chocolate.
So, the number of double cones they can make is:
Ed: 3 choices
Friend 1: 2 choices
Friend 2: 2 choices
Friend 3: 2 choices
Friend 4: 2 choices
Total number of double cones = 3 * 2 * 2 * 2 * 2 = 48 cones
Case 3: Triple cones
In this case, each person can choose three flavors for their cone.
Ed has 3 choices (chocolate, vanilla, or strawberry).
His four friends (excluding Stacey) have 3 choices each (chocolate, vanilla, or strawberry) since they are not restricted like Stacey.
So, the number of triple cones they can make is:
Ed: 3 choices
Friend 1: 3 choices
Friend 2: 3 choices
Friend 3: 3 choices
Friend 4: 3 choices
Total number of triple cones = 3 * 3 * 3 * 3 * 3 = 243 cones
Now, to find the total number of different kinds of cones they can make, we add up the single, double, and triple cones:
48 (single cones) + 48 (double cones) + 243 (triple cones) = 339 cones.
Therefore, they can make 339 different kinds of cones.
Number sentences supporting the conclusions:
- The number of single cones = 3 * 2 * 2 * 2 * 2 = 48 cones.
- The number of double cones = 3 * 2 * 2 * 2 * 2 = 48 cones.
- The number of triple cones = 3 * 3 * 3 * 3 * 3 = 243 cones.
- Total number of different kinds of cones = 48 + 48 + 243 = 339 cones.