Word problem (solve using elimination

Question

A Big Ten football team is going to a bowl game. Junior and senior students will

fill 14 vans and 6 buses with 408 students. Freshman and sophomore students will fill 7

vans and 1 bus with 105 students. Find the number of students in each van and in each bus.

Answer 1

OK this is a simple systems of equations problem. First no matter what your grade level is, a student will take up one seat, therefore, it does not matter that a student is a Senior, junior, sophomore or freshman. Then the variables are only 2 how many students a bus carries B or how many students Van carries V so we know that 14V +6B = 408 and 7V +B =105, by multiplying our second equation by -2 getting -14V -2B = -210 this makes the equations poised to solve by elimination, add each variable on the 2 equations together getting 0V +4B = 198 getting 49.5 students per bus, this is a dilemma, there cannot be half a student, If you could show me the source of the question I might be able to solve it better. You or whoever wrote this problemhave made an error probably in the values, I triple checked my own work, so either the 408 or 105 or any other value is incorrect. However lets assume the case is 49.5 and toss al logic aside. given that in this trip the TOTAL number of buses was 7, you get 7 * 49.5 meaning 346.5 students were sent by bus. the reaming students (166.5) were sent by van so we divide 166.5/ 21(21 van total) getting us 7.928 students. I dont know what 0.928 of a student is....