Question

I am in a algebra 1 class and we are learning about variables and slope and all that stuff , and also were mainly talking about the substitution method and elimination method .. and I do not understand nothing at all. the question is " this year the senior class at high school A and high school B both planned tries. There senior class for high school A rented and filled 8 vans and 8 buses with 240 students, high school B rented and filled 4 vans and 1 bus with 54 students. Every van had the same number of students in it as did the bus. Find the number if students in each van in each bus" ... I am completely lost ..

Answer 1

Let's define the next variables:

v: number of students in a van

b: number of students in a bus

The senior class for high school A rented and filled 8 vans and 8 buses with 240 students, that is,

8v + 8b = 240 (eq. 1)

High school B rented and filled 4 vans and 1 bus with 54 students, that is,

4v + b = 54 (eq. 2)

Isolating b from equation 2,

4v + b = 54

b = 54 - 4v

Replacing this result into equation 1,

8v + 8(54 - 4v) = 240

8v + 8(54) - 8(4v) = 240

8v + 432 - 32v = 240

-24v + 432 = 240

-24v = 240 - 432

-24v = -192

v = -192/-24

v = 8

Then,

b = 54 - 4(8)

b = 54 - 32

b = 22

There are 8 students in each van, and 22 students in each bus