New York City 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 3 vans and 14 buses with 509 students. High School B rented and filled 12 vans and 10 buses with 472 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.

Step-by-step explanation:

Let's say :

v = number students in van, b = number of students in bus

From the info provided in the question:

High school A takes 3 vans and 14 buses for 509 students

We can write this as:

3v + 14b = 509

You can re-write this as :

3v = 509 - 14b

We also know High School B takes 12 vans and 10 buses for 472 students:

12v + 10b = 472

Since we already know that 3v = 509 - 14b , substitute this equation into the above formula and you get:

12v + 10b = 472

4(509 - 14b) + 10b = 472

2036 - 56b + 10b = 472

2036 - 46b = 472

2036 - 472 = 46b

1564 = 46b

Divide both sides by 46 to find "b".

b = 1564/ 46 =  34

Therefore the number of students that fit in each bus is 34.

So since we know b = 34, substitute b into the equation at the top:

3v = 509 - 14b

3v = 509 - 14(34)

3v = 509 - 476 = 33

Divide both sides by 3 to find "v".

v = 33/3 = 11.

Therefore the number of students in each van is 11.

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step-by-step explanation: