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The senior classes at High School A and High School B planned seperate trips to Austin, TX.
The senior class at Hogh 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 each bus carried the same number of students.
How many student can a van carry? How many student can a bus carry?
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Let v = # of students on one van; let "b" = # of students on one bus.
Then from the condition, you have this system of 2 equations in 2 unknowns
1*v + 6*b = 372, (1)
4*v + 12*b = 780. (2)
Multiply q(1) by 2 (both sides). The modified system is
2v + 12b = 744, (3)
4v + 12b = 780. (4)
Now subtract eq(3) from eq(4) (both sides). The terms "12b" will cancel each other, and you will get
a single equation for "v" (It is how the Elimination method works):
4v - 2v = 780 - 744,
2v = 36 ====> v = = 18.
So, one van carries 18 students.
Then from eq(1) 6b = 372-18 = 354 ====> b = = 59.
Answer. One van carries 18 students. One bus carries 59 students.
Solved.
On the way, you learned on how the Elimination method works.