Math Problem help please?

Question

The students in Junior high school are planing a trip to visit the new york Hall of science in queens. 193 students have turned in their permission slips and are going to the trip. There are two types of vehicles available- a school bus and mini-van. the school buses seat 51 students each and the mini-vans seat 8 students each. How many school buses and mini-vans are needed if there are only eight drivers available?

what are the independent variables? and what are the dependent variables?

Answer 1

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The independent variable could, arguably, be the number of students, the number of drivers, or how many students fit in a mini-van or school bus.
The dependent variable would be the number of buses and vans.

To solve this you will need to set up a system of equations.
Let x= number of buses
y= number of vans

51x + 8y = 193
x + y =8

There are many ways to solve this; here is one:
Multiply the second equation by 8 and get:
51x + 8y = 193
8x + 8y =64

Now subtract the equations:

51x + 8y = 193
- (8x + 8y =64)
------------------------
43x=129
x= 3

Now plug 3 for x in either equation to get y:
x + y =8
(3) + y = 8
y=5

The solution is 3 buses and 5 vans.

Source(s):

AP Calculus

Answer 2

M + B = 8 (drivers for each type)
8M + 51B = 193 (seating). Now multiply the 1st eq by 8:
8M + 8B = 64, and subtract:
43B = 129, B = 3, M = 5
(Of course, if they used 4 buses, they wouldn't need the 4 other drivers.)

Answer 3

Ok this is a very simple question.
Ok remember there are 8 drivers.
so lets say we wanted to use 2 buses, that requires 2 drivers. now we have 6 drivers left all to drive mini vans. So, 2 buses= 102 and 6 minivans=48 students. that equals 150 students, but thats not enough. If you had four buses that would only be four drivers and already more than enough seats. So now we know we must have 3 buses which equals 153 seats. That leaves 5 drivers left. 5 drivers for 5 minivans which hold 8 people. so very simply

3 bus drivers= 153 seats for students
5 minivan drivers= 40 students

153+40=193 perfect amount
3 bus drivers plus 5 minivan drivers =8 drivers

Answer 4

your first step is to make two equations.
we will make b=school buses and v=mini-vans

equation 1: 51b+8v=193
because each bus holds 51 students and each van holds 8 students, with a total need of seating for 193 students.
equation 2: 1b+1v=8
because the bus and the van each only need one driver and there are a total of 8 drivers available.

then you need to get rid of one of the variables in the equations, so multiply the second equation by -8
(-8)(1b+1v=8) getting a new equation of (-8b+-8v=-64)
then add the equations together

{ 51b + 8v = 193 }
{+ -8b + -8v = -64 }
{------------------------- }
{ 43b + 0v = 129 }

now you need to solve for the variable by dividing each side by 43, getting b=3

now plug that answer for b into the other equation, 1b+1v=8 so its now 3+1v=8. subtract the 3 from both sides leaving you with v=5.

now you know that you need 3 school buses and 5 mini-vans to transport 193 students with only 8 drivers

check: (plug the answers into the original equations)
51(3)+8(5) = 193 true
1(3)+1(5) = 8 true

sorry if this is hard to follow, it wasn't very easy to try to type all the equations and work them out while explaining.

Source(s):

love mathematics :)