the local amusement park is a popular field trip destination. this year the senior class at high school a and the senior class of highscool b both planned trips there. the senior class at highschool a rented and filled 12 vans and 13 busses with 672 students. highschool b rented and filled 14 vans and 13 busses with 706 students. each van and bus carried the same number of students. how many students can a van carry? how many students can a bus carry?

A van can carry 17 students and a bus can carry 36 students.

Step-by-step explanation:

To solve for two different variables, in this case 'v' = the number of vans and 'b' = the number of buses, we can set up a system of equations and use elimination to solve. Our first equation would be 12v + 13b = 672 and our second equation would be 14v + 13b = 706. In order to use elimination, I first need to multiply one of the equations by - 1 in order to eliminate the 'b' variable. If I multiply the entire first equation by - 1, I get - 12v - 13b = - 672. I then add the first and second equation together to get 2v = 34, or v = 17. Now that I know that number of vans, I can put 17 into my equation for 'v' and solve for 'b'. 12x17 + 13b = 672, 204 + 13b = 672 (subtract 204 from both sides), 13b = 468 (divide both sides by 13), b = 36.