Question

The senior class at high school A and High school B planned separate trips to the county fair. The senior class at high school A rented and filled 11 vans and 1 bus with 256 students. High school B rented and filled 1 van and 12 busses with 714 students. Every van had the same number of students in it as did the busses. How many students can the van carry? How many students can a bus carry?

a) Van can carry 32 students, bus can carry 32 students.
b) Van can carry 22 students, bus can carry 19 students.
c) Van can carry 24 students, bus can carry 59 students.
d) Van can carry 56 students, bus can carry 59 students.

Answer 1

The problem can be answered by setting up a system of linear equations to find the number of students each van and bus can carry and by solving this system to find the capacity of each vehicle.

Step-by-step explanation:

The question involves solving a system of linear equations based on numerically encoding a word problem. The word problem describes two high schools renting vehicles with a given number of students. We are given that high school A rented 11 vans and 1 bus for 256 students, while high school B rented 1 van and 12 buses for 714 students. Assuming vans and buses carry the same number of students respectively, we need to determine the capacity of each.

Let's denote the number of students per van as v and the number of students per bus as b. Now we can establish two equations based on the information given:

• 11v + 1b = 256 (Equation A)
• 1v + 12b = 714 (Equation B)

We can solve this system of equations to find the values of v and b.