Number of students in each van and in each bus

Question

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 3 vans and 10 buses with 286 students high school b rented and filled 6 vans and 10 buses with 322 students each van and each bus carried the same number of students find the number of students in each van and in bus

Answer 1

3v + 10b = 286

6v + 10b = 322

Because the system of equations has a common coefficient (10), we can use the elimination method to solve.

3v + 10b = 286

-1(6v + 10b = 322) = -6v - 10b = -322

3v + 10b = 286

-6v - 10b = -322

Combine the two equations and solve for v.

-3v = -36

Divide both sides by -3.

-3v/-3 = -36/-3

v=12

Then solve for b using the solution we calculated for v.

3v +10b = 286

3(12) + 10b = 286

36 + 10b = 286

Subtract 36 from each side of the equals sign.

36-36 + 10b = 286-36

10b= 250

Divide by 10 on each side of the equals sign.

10b/10 = 250/10

b=25

Each van holds 12 students.

Each bus holds 25 students