Solving linear systems using technology

Question

The senior classes at high school A and high school B planned separate trips to the state fair. The senior class at high school A rented and filled 2 vans and 8 busses with 360 students. High school B rented and filled 6 vans and 1 bus with 114 students. Each van and each bus carried the same number of students. Find the number of students in each van and bus.

Answer 1

Hi Adrianna,

First you would need to come up with a system of equations.

lets say the number of students in each van is X and number of students in each bus is y, based on that this is the system of equations:

2x+8y=360 (high school A)

6x+y=114 (high school B)

We will use substitution to solve this. Lets solve the second equation for y and plug it into the first equation.

6x+y=114 (subtract 6 x from both sides)

y=114-6x, now lets plug this into the first equation

2x+8(114-6x)=360, then distribute the 8 and you get

2x+912-48x=360, combine the like terms

-46x+912=360, subtract 912 from both sides

-46x=-552, divide both sides by -46

x=12, now we will plug this into the second equation to solve for y

6*12+y=114

72+y=114, subtract 72

y=42

So the number of students in each van is 12 and in each bus is 42.

Answer 2

2V + 8b = 360

6v + 1 b = 114 --> b = 114-6v

2v + 8(114-6v) = 360

2v + 912 - 48v = 360

-46v + 912 = 360

-46v = 360-912

-46v = -552

v =12

then b = 114-6v = 114-6(12)

= 114-72

= 42

42 students on the bus

12 in the van...