Senior class at 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 has the same number of students in it as did the buses. Find the number of students in each van and in each bus

Each van had 8 students and each bus had 22 students

Step-by-step explanation: We shall start by assigning a letter to represent the unknown variables in this question. Each bus shall be represented by by B while each van shall be represented by V. So if in high school A, 8 vans and 8 buses were filled with 240 students in total, we can derive the expression

8V + 8B = 240. Also if in high school B, 4 vans and 1 bus were filled with 54 students in total, we can as well derive the following expression,

4V + B = 54

What we have at this point is a pair of simultaneous equations with unknown variables V and B

8V + 8B = 240 —————(1)

4V + B = 54 ——————-(2)

From equation (2), we shall make B the subject of the equation. Hence

B = 54 - 4V

We can now substitute for the value of B into equation (1) and equation (1) can now be written as

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

8V + 432 - 32V = 240

By collecting like terms we now have

8V - 32V = 240 - 432

(Note that when a positive value crosses to the other side of an equation it becomes negative and vice versa)

-24V = -192

Divide both sides of the equation by -24

V = 8

That means there 8 students in each van. Now we substitute for the value of V into equation (2)

4V + B = 54

4(8) + B = 54

32 + B = 54

Subtract 32 from both sides of the equation

32 - 32 + B = 54 - 32

B = 22

That means there were 22 students in each bus.

Therefore each van had 8 students and each bus had 22 students

no solution

step-by-step explanation:

there is not enough information in the problem to solve.

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,