In your journal, you identified careers that involve irrational numbers. You brainstormed or researched jobs that use pi or Euler’s number to do their work.
Imagine that your friend loves to plan parties, and he wants to be an event planner someday. He does not think he needs to know how to find a number between two rational numbers. He also says he will never use pi again in his life after math class. You think of some of the tasks he might need to do as an event planner:
Decide how many cakes to order when a party could have as few as 50 people and as many as 100 people.
As an event planner, your friend would certainly need to know how to find a number between two rational numbers in order to determine how many cakes to order for a party that could have as few as 50 people and as many as 100 people. The number of cakes would need to be an integer value, as you cannot order a fraction of a cake.
To make a well-informed decision, he would need to calculate the average number of guests expected and ensure that he orders enough cakes to accommodate the maximum number of attendees. This involves finding a rational number between the two given numbers (50 and 100) that represents the average or median expected attendance.
For example, if he estimates the average number of guests to be around 75, he would need to order enough cakes to serve this number of people. However, it is always a good idea to add some extra cakes to account for unexpected guests or last-minute changes.
Understanding how to find a number between two rational numbers would help your friend make accurate estimates and ensure he provides adequate resources for the party he plans.
Choose a round table that is the correct size to fit six people.
To choose the correct size round table to fit six people, your friend would need to have an understanding of geometry and spatial reasoning. Here are a couple of considerations they should keep in mind:
1. Seating Arrangement:
- For a round table, it is common to arrange chairs evenly spaced around the perimeter to ensure everyone has equal access to conversation and food.
- If your friend wants to have all six people sitting on one side of the table, they can choose a smaller table diameter. However, it is usually more comfortable for everyone to sit around the entire circumference of the table.
2. Space Requirement:
- Each person typically requires around 24 to 30 inches of space width-wise to sit comfortably without feeling crowded.
- To allow room for dishes, centerpieces, or any additional items on the table, your friend might want to add an extra 6 to 12 inches to each person's space.
Considering these factors, they can estimate the table size as follows:
- Assuming a minimum width requirement of 24 inches per person, the circumference of the table needed would be approximately 6 persons × 24 inches = 144 inches.
- Using the formula for the circumference of a circle (C = 2πr), they can calculate the table's diameter (d) as follows: d = C/π = 144 inches/3.14 ≈ 45.86 inches.
- Rounding up to the nearest manageable table diameter, your friend could choose a round table with a diameter of 48 inches.
Therefore, a round table with a diameter of 48 inches would be an appropriate size to comfortably seat six people.
As an event planner, your friend would indeed need to make calculations involving rational numbers. Here's a step-by-step process for calculating how many cakes to order for a party with a variable number of attendees:
1. Determine the minimum and maximum number of people who might attend the party. In this case, the minimum is 50 and the maximum is 100.
2. Find the average number of people expected to attend the party. Add the minimum and maximum numbers and divide the sum by 2: (50 + 100) / 2 = 75.
3. Consider the size of the cakes available. Let's say each cake is designed to feed 10 people.
4. Divide the average number of people by the number of people a cake can feed to determine the number of cakes needed. In this case, 75 / 10 = 7.5.
5. Since you can't have half a cake, you'll need to round up to the nearest whole number. So, your friend should order 8 cakes to accommodate the expected number of attendees at the party.
It's important for your friend to understand how to find a number between two rational numbers in scenarios like this, as precision in event planning can help avoid over or underestimating the resources needed for a successful party. Additionally, he may encounter other situations where familiarity with rational numbers is necessary, such as budgeting, negotiating prices for venues or services, and managing guest lists.