Question

The two high schools in your district plan a trip to New York City. Your high school rents and fills i van and
7 buses with 180 students. The other high school rents and fills 6 vans and 6 buses with 216 students. There
are no open seats in any van or bus. Define your variables and create an equation to model each situation
How many students can a van carry? How many students can a bus carry?​

Answer 1

Answer:

Van 12 students, Bus 24 students

Step-by-step explanation:

Let the number of students that a van can carry is "x" and the number of students a bus can carry is "y"

According to the given data, 1 van and 7 buses carry 180 students.

Since, number of students in one van is "x" and number of students in one bus is "y", the number of students in 1 van and 7 buses would be x + 7y. So, we can set up the equation as:

x + 7y = 180                                           Equation 1

Also,

6 vans and 6 buses can carry 216 students. 6 vans will carry 6x students 6 buses will carry 6y students, so we can set up the second equation as:

6x + 6y = 216

Dividing both sides by 6, we get:

x + y = 36                                             Equation 2

Subtracting Equation 2 from Equation 1, we get:

x + 7y - (x + y) = 180 - 36

x + 7y - x - y = 144

6y = 144

y = 24

Using the value of y in Equation 1, we get:

x + 7(24) = 180

x + 168 = 180

x = 12

Since, x represents the number of students a van can carry and y represents the number of students a bus can carry, we can conclude:

A van can carry 12 students and a bus can carry 24 students.