Math Problem Statement

The passengers on an excursion bus consisted of 14 married couples, 8 of whom brought no children and, 6 of whom brought 3 children a piece. Counting the driver, the bus has 31 occupants How is this possible?

Solution

Let's analyze the numbers carefully.

  1. There are 14 married couples on the bus.

    • 8 couples did not bring children.
    • 6 couples each brought 3 children.
  2. The total number of children:

    • Since 6 couples brought 3 children each, we calculate:
      6×3=18 children6 \times 3 = 18 \text{ children}
  3. Total number of adults:

    • There are 14 couples, so the number of adults is:
      14×2=28 adults14 \times 2 = 28 \text{ adults}
  4. Adding the driver:

    • The total number of people on the bus is:
      28 (adults)+18 (children)+1 (driver)=3128 \text{ (adults)} + 18 \text{ (children)} + 1 \text{ (driver)} = 31

Thus, the numbers add up correctly, making it possible for the bus to have 31 occupants.


Do you want further clarifications or breakdowns?

Here are 5 related questions you might find interesting:

  1. If a different set of 4 couples had brought 2 children each, how many total occupants would be on the bus?
  2. How would the number of passengers change if 3 more couples joined, each bringing 2 children?
  3. If the bus had a seating capacity of 40, how many more people could it accommodate?
  4. What fraction of the bus occupants are children?
  5. If each child paid half the fare of an adult, what would be the total fare collected if an adult ticket costs $20?

Tip:

When solving word problems, always break down the given information into categories and systematically count each group.

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Math Problem Analysis

Mathematical Concepts

Basic Arithmetic
Counting Principles

Formulas

Total People = (Adults) + (Children) + (Driver)

Theorems

Basic Counting Principle

Suitable Grade Level

Grades 5-7