In the space below define your variables, write a system of equations and solve.
The senior class at high school A and high school B planned seperate trips to New York city. High school A rented and filled 14 vans and 2 busses with 258 students. High school B rented and filled 7 vans and 12 busses with 778 students. Every van and every bus had the same number of students in it. Find the number of students in each van and in each bus.
Let's define the variables:
Let x be the number of students in each van.
Let y be the number of students in each bus.
We can write the following system of equations:
Equation 1: 14x + 2y = 258
Equation 2: 7x + 12y = 778
To solve this system of equations, we can use the method of substitution or elimination.
Method of Substitution:
Solve equation 1 for x:
14x = 258 - 2y
x = (258 - 2y)/14
Substitute x in equation 2 with (258 - 2y)/14:
7(258 - 2y)/14 + 12y = 778
Multiply both sides by 14 to eliminate the denominators:
7(258 - 2y) + 168y = 778*14
1806 - 14y + 168y = 10892
154y = 9102
y = 9102/154
y = 59
Substitute y = 59 back into equation 1 to solve for x:
14x + 2(59) = 258
14x + 118 = 258
14x = 258 - 118
14x = 140
x = 140/14
x = 10
So, there are 10 students in each van and 59 students in each bus.