Class A: 6v + 8b = 202 Class B: 12v + 16b = 284 Solve using the elimination method: since 6v and 12v are perfect for elimination, multiply the class A equation by 2 so that the van variable cancels out: 12v + 16b = 404 12v + 10b = 284 Then subtract the bottom equation from the top: 6b = 120 b = 20 Now you know that each bus can hold 20 students. Just plug this into one of the original equations to solve for vans: 6v + 8(20) = 202 6v + 160 = 202 6v = 42 v=7 So then you know that each van can hold 7 students. Check: 12 (7) + 10 (20) = 284
The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 6 vans and 8 buses with 202 students. High School B rented and filled 12 vans and 10 buses with 284 students. Each van and each bus carried the same number of students. How many students can a van carry?How many students can a bus carry? please show work thank you.