Question

The senior classes at high school A and high school B planned separate trips to New York City. The senior class at high school A rented and filled 10 vans and 2 buses with 198 students. High School B rented and filled 13 vans and 6 buses with 390 students. Each van and each bus carried the same number of students. How many students can a van carry, and how many students can a bus carry?

A. A van can carry 15 students, and a bus can carry 30 students.
B. A van can carry 10 students, and a bus can carry 15 students.
C. A van can carry 18 students, and a bus can carry 12 students.

Answer 1

To find the number of students that a van can carry and the number of students that a bus can carry, we need to solve a system of equations.

Step-by-step explanation:

To find the number of students that a van can carry and the number of students that a bus can carry, we need to set up a system of equations. Let's call the number of students a van can carry 'x' and the number of students a bus can carry 'y'.

From the given information, we know that 10 vans + 2 buses = 198 students and 13 vans + 6 buses = 390 students. We can write the following system of equations:

10x + 2y = 198

13x + 6y = 390

To solve this system, we can multiply the first equation by 3 and subtract it from the second equation multiplied by 2:

(2)(10x + 2y) - (3)(13x + 6y) = (198)(2) - (390)(3)

20x + 4y - 39x - 18y = 396 - 1170

-19x - 14y = -774

Simplifying, we get:

19x + 14y = 774

Solving this equation and the first equation simultaneously will give us the values of 'x' and 'y'.