Question

Yellowstone National Park is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 5 vans and 2 buses y with 115 students. High School B rented and filled 1 van () and 6 buses () with 163 students. Each van carried the same number of students and each bus carried the same number of students. Write equations to represent the scenario. Then, graph to find the number of students in each van and in each bus.

Answer 1

Each van carries 13 students and each bus carries 25 students.

Distribution

Given that the senior class at High School A and the senior class at High School B both planned trips to Yellowstone, and the senior class at High School A rented and filled 5 vans and 2 buses with 115 students, while High School B rented and filled 1 van and 6 buses with 163 students, and each van carried the same number of students and each bus carried the same number of students, to determine the number of students in each van and in each bus, the following calculation must be made:

• 5X + 2Y = 115
• 1X + 6Y = 163
• 5X + 2Y = 115
• 5X + 30Y = 815
• 815 - 115 = 28Y
• 700 = 28Y
• Y = 700 / 28
• y = 25
• 1X + 6x25 = 163
• 1X = 163 - 150
• X = 13

Therefore, each van carries 13 students and each bus carries 25 students.

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