Answer:
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.
