Math Problem Statement

A restaurant offers 10 entrée choices and 5 side dishes, with a choice of dessert. If there are 200 possible meal options, how many desserts are there to choose from?

Solution

Let's analyze the problem.

The restaurant offers:

  • 10 entrée choices
  • 5 side dishes
  • An unknown number of desserts, which we’ll call dd

The total number of possible meal options can be calculated as: Total meal options=(number of entreˊe choices)×(number of side dishes)×(number of desserts)\text{Total meal options} = (\text{number of entrée choices}) \times (\text{number of side dishes}) \times (\text{number of desserts}) We are given that the total number of meal options is 200. Therefore, we have: 10×5×d=20010 \times 5 \times d = 200 Now, solving for dd: 50×d=20050 \times d = 200 d=20050d = \frac{200}{50} d=4d = 4

So, there are 4 dessert choices available.

Would you like more details or have any further questions?

Here are 5 related questions to expand your understanding:

  1. What happens to the total meal options if the number of side dishes is doubled?
  2. How many total meal combinations would there be if the restaurant added 2 more dessert choices?
  3. If there were 12 entrée choices, how would that affect the number of desserts needed for 300 possible meal combinations?
  4. How would you calculate the number of possible meal options if two side dishes could be selected instead of one?
  5. What would be the total options if the number of entrée choices was reduced to 8?

Tip: Multiplication is a quick way to find the total number of combinations when choices are independent, like entrées, side dishes, and desserts in this scenario.

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Math Problem Analysis

Mathematical Concepts

Multiplication of Combinations
Algebra

Formulas

Total meal options = (number of entrée choices) × (number of side dishes) × (number of desserts)
10 × 5 × d = 200

Theorems

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Suitable Grade Level

Grades 6-8