Question

the senior classes of high school A and high school B planned separate trips to the state fair. the senior class at high school A rented and filled 3 vans and 10 buses with 298 students. high school b rented and filled 12 vans and 7 buses with 367 students. each van and each bus carried the same amount of students. find the number of students in each van and in each bus.

Answer 1

25 students in each bus, 16 students in each van

Explanation:

x = vans

y = buses

`3x + 10y = 298\\\\12x + 7y = 367`

Multiply the top equation by -4 to turn 3x into -12x

`-12x - 40y = -1192\\12x + 7y = 367`

Cancel out -12x and 12x

`-40y = -1192\\7y = 367`

Add the terms together

`-33y = -825\\y = 25`

We know that 25 students can fit in each bus

`3x + 10(25) = 298\\3x + 250 = 298\\3x = 48\\x = 16`

16 students can fit in each van