Question

1. Mindy's high school class has a total of 150 students and they are planning a field trip. The school has

small buses and vans to transport all students. Each van can seat 8 students and each bus can seat 14
students. There are only 15 drivers, so the total number of vehicles that they can take must be 15. How
many of each vehicle will Mindy's qass need to transport everyone?!
a. Write a system of equations to describe the situation.

Answer 1

Mindy's class requires 10 vans and 5 buses to transport 150 students, given the seating capacities and the limitation of 15 drivers available for the trip.

Step-by-step explanation:

To solve Mindy's class transportation problem using a system of equations, we first need to define our variables. Let's let v represent the number of vans and b represent the number of buses. We are given that each van can seat 8 students and each bus can seat 14 students, and the total number of vehicles cannot exceed 15 since there are only 15 drivers. Additionally, the total number of students to transport is 150. With this in mind, we can set up the following system of equations:

v + b = 15 (because there are 15 vehicles available).

v = 10 (number of vans).

Mindy's class will need 10 vans and 5 buses to transport all the students.

Answer 2

Step-by-step explanation:

150 students van holds 8 students small bus holds 14 students

with only 15 drivers you can only have 15 vehicles

v = vans b = buses

eq 1) v + b = 15

eq 2) 8v + 14b = 150

eq 1) into eq 2) the combined equations

v = 15 - b ----> 8v + 14b = 150 ----> 8(15 - b) + 14b = 150

8(15 - b) + 14b = 150 solve for b

120 - 8b + 14b = 150 collect terms and subtract 120 from both sides

120 -120 + (14 - 6)b = 150 -120

6b = 30

b = 30/6

b = 5

noe find the number of vans

v + b = 15

v = 15 - b

v = 15 - 5

v = 10