The senior classes at High School A and High School B planned separate trips to Yellowstone

The senior classes at High school A and high school B planned separate trips to NYC. The senior class at high school A rented and filled 1 van and 6 buses with 372 students. High school B rented and filled 4 vans and 12 buses with 780 students. Each van and bus carried the same number of students. How many students can a van and a bus carry?

Answer provided by our tutors

let

b = the number of students a bus can carry

v = the number of students a van can carry

The senior class at high school A rented and filled 1 van and 6 buses with 372 students

v + 6b = 372

High school B rented and filled 4 vans and 12 buses with 780 students

4v + 12b = 780 divide both sides by

v + 3b = 195

by solving the system of equations

v + 6b = 372

v + 3b = 195

we find

v = 18 students

b = 59 students

click here to see the step by step solution of the system of equations

Click to see all the steps

A van can carry 18 students.

A bus can carry 59 students.

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Question 947295: Yellowstone national park is a popular field trip destination. This year the senior class High school A an the senior class at high school B both planned trips there. The senior class at high school A rented and filled 7 vans and 14 buses with 504 students. High school B rented and filled 14 vans and 13 buses with 588 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus?
Found 2 solutions by stanbon, josgarithmetic:

Answer by stanbon(75887)

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You can put this solution on YOUR website!
Yellowstone national park is a popular field trip destination. This year the senior class 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 7 vans and 14 buses with 504 students. High school B rented and filled 14 vans and 13 buses with 588 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus?
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Equations:
7v + 14b = 504 students
14v + 13b = 588 students
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Modify for elimination::
14v + 28b = 2*504
14v + 13b = 588
----------------
Subtract and solve for "b"::
15b = 420
b = 28 (# of students in each bus)
----
Solve for "v"::
7v + 14b = 504
7v + 14*28 = 504
7v = 112
v = 16 (# of students in each van)
===============
Cheers,
Stan H.
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Answer by josgarithmetic(37916)

(Show Source):

You can put this solution on YOUR website!
Assign variables like v for how many students per van, and b for how many students per bus.

CLASS A:
7v+14b=504

CLASS B:
14v+13b=588

IF you multiply the A equation by 2, then you can form a system,

perfectly set for eliminating the v terms and quickly finding value for b.

The senior classes at High School A and High School B planned separate trips to Yellowstone National Park. The senior class at High School A rented and filled vans and buses with students. High School B rented and filled vans and buses with students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many students can a bus carry?
Van: , Bus:
Van: , Bus:
Van: , Bus:
Van: , Bus:

Philip P. answered • 12/26/14

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Let x = the number of student that a van can carry and y = the number that a bus can carry.