The two high schools in your district plan a trip to New York City. Your high school rents and fills i van and7 buses with 180 students. The other high school rents and fills 6 vans and 6 buses with 216 students. Thereare no open seats in any van or bus. Define your variables and create an equation to model each situationHow many students can a van carry? How many students can a bus carry?
Accepted Solution
A:
Answer:Van 12 students, Bus 24 studentsStep-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 1Also,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 = 216Dividing both sides by 6, we get:x + y = 36 Equation 2Subtracting Equation 2 from Equation 1, we get:x + 7y - (x + y) = 180 - 36x + 7y - x - y = 1446y = 144y = 24Using the value of y in Equation 1, we get:x + 7(24) = 180x + 168 = 180x = 12Since, 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.