Math Problem Statement

A group of 280 elementary school students and 40 adults are going on a field trip. They are planning to use two different types of buses to get to the destination. The first type of bus holds 50 people and the second type of bus holds 56 people. Andre says that 3 of the first type of bus and 3 of the second type of bus will hold all of the students and adults going on the field trip. Is Andre correct?

Solution

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Question Overview:

  • There are 280 elementary students and 40 adults going on a field trip, making a total of 320 people.
  • Two types of buses are available:
    • The first type of bus holds 50 people.
    • The second type of bus holds 56 people.
  • Andre claims that using 3 of each type of bus will accommodate all 320 people.

Step-by-Step Solution:

  1. Calculate the total number of people that can fit on the buses Andre suggests:

    • 3 buses of the first type can hold: 3×50=1503 \times 50 = 150 people.
    • 3 buses of the second type can hold: 3×56=1683 \times 56 = 168 people.
  2. Calculate the total number of people that these buses can carry: 150+168=318 people150 + 168 = 318 \text{ people}

  3. Compare with the total number of people needing transport:

    • The total number of people is 320.
    • The buses Andre suggests can only carry 318 people, which is 2 people short.

Conclusion:

Andre is not correct because the total capacity of 6 buses (3 of each type) is 318, while 320 people need to be transported.

Would you like more details on the calculations or any other explanation?

Here are 5 questions for further practice:

  1. What would happen if Andre used 4 of the second type of bus instead?
  2. How many buses would Andre need if only using the first type of bus?
  3. How many buses would be needed if only using the second type of bus?
  4. If Andre wants exactly 320 people on the buses, what is the minimum number of buses needed?
  5. How many people would 4 of the first type of bus and 2 of the second type of bus carry?

Tip: Always check the total capacity when planning any transportation problem to ensure all people are accommodated.

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Math Problem Analysis

Mathematical Concepts

Algebra
Word Problems
Multiplication
Addition

Formulas

Total number of people = number of buses of type 1 * capacity of type 1 bus + number of buses of type 2 * capacity of type 2 bus

Theorems

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Suitable Grade Level

Grade 7-8