Algebra 1 Systems of Equations

Question

The senior class at High school A and senior class at High School B both planned a trip. Highschool A rented and filled 11 vans and 7 buses with 459 students. Highschool B rented and filled 16 vans and 10 buses with 660 students. Find the number of students in each van and bus

Answer 1

For this question, we obviously assume that each school is using the same sizes or vans and buses. If we let v be the number of students in each van and b be the number of student on each bus, we know from high school A's information that 11v+7b=459.

Similarly, we know from high school B's information that 16v+10b=660. Let's write these two equations as a system:

11v+7b=459

16v+10b=660

We want to make some variables cancel. Let's multiply the top equation by 10 and the bottom equation by 7 to try and cancel out the b terms.

110v+70b=4590

112v+70b=4620

Subtracting the above equations from each other yields −2v=−30, which means v=15.

Substituting this back into the original top equation,

11(15)+7b=459

7b=459−165

7b=294

b=42

Thus, there are 15 students per van and 42 students per bus!