SOLUTION: 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 cl

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) (Show Source): 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
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Subtract and solve for "b"::
15b = 420
b = 28 (# of students in each bus)
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Solve for "v"::
7v + 14b = 504
7v + 14*28 = 504
7v = 112
v = 16 (# of students in each van)
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Cheers,
Stan H.
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Answer by josgarithmetic(39618) (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.
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