The senior classes 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 5 vans and 6 buses with 393 students. High School B rented and filled 7 vans and 6 buses with 411 students. Each van and each bus carried the same number of students. Define two variables for this situation. Write a system of equations to represent this situation. How many students can a van carry? How many students can a bus carry?

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reeserl reeserl · Answer 1 · 2021-02-21T00:31:16+01:00

Answer:

Let v = no. of students in a van

b = no. of students in a bus

5v + 6b = 393 7v + 6b = 411

9 students in each van 58 students in each bus

Step-by-step explanation:

Let v = no. of students in a van

b = no. of students in a bus

School A School B

(1) 5v + 6b = 393 (2) 7v + 6b = 411

Change all the signs in (1) to get -5v - 6b = -393

Add that to (2) 7v + 6b = 411

-5v - 6b = -393

2v = 18

v = 9 students in each van

Substitute 9 in for v in (1) and we get 5(9) + 6b = 393

45 + 6b = 393

6b = 348

b = 58 students in each bus