Please helppp

Question

the county fair is a popular field trip destintion. This year the senior class at High School Aand the senior class of High School B both planned trips there. the Senior class of High School A rented and filled 14 vans and 3 buses with 171 students.High School B rented and filled 4 vans and 9 buses with 285 students. Every van had the same number of studentsin it, as did the buses. How many students can a van carry? How mant students can a Bus carry?

Answer 1

v = number of vans

b = number of busses

 

14v + 3 b = 171

4v + 9 b = 285

 

Multiply top equation by 3

 

42v + 9b = 513

4v + 9b = 285

 

Subtract bottom from top

 

38v = 228

v = 6

 

Substitute into second equation above

 

4(6) + 9b = 285

24 + 9b = 285

9b = 2

b = 29

 

Each van hold 6 students and each bus holds 29. 

 

Answer 2

this is a system of equations: 

 

X = students in busses

y = students in vans

 

for High school A : 14y + 3x = 171

for High school B:    4y + 9x = 285

 

Let's multiply through the first equation by -3 and then add the two equations together. 

 

-42y -  9x = -513

   4y + 9x =  285

-38y         = -228

    y        =  6

 

now let's plug the value for y into the second equation: 

4(6) + 9x = 285

24 + 9x = 285

9x = 261

x = 29

 

So now we know how many students each type of vehicle carries. We can check to see if our answer matches the description at the beginning: 

 

At HS A: 14 Vans each with 6 students = 14*6 = 84 

               3 Busses each with 29 students = 3 * 29 = 87

                84 + 87 = 171 students total 

 YEAH -- it checks. 

 

Can you check for HS B?