Question

Two schools took a trip to the state fair. Morel High School rented 10 vans and 3 buses to

transport 328 students. Jams High School rented 5 vans and 6 buses to transport 416
students. If all vehicles were filled, how many students were transported by bus? By van?
Let x be bus capacity and let y be van capacity.

Answer 1

Answer: Morel High School transported 3 buses and 10 vans, which is a total of 324 = 72 students on buses and 104 = 40 students on vans. Jams High School transported 6 buses and 5 vans, which is a total of 624 = 144 students on buses and 54 = 20 students on vans. So in total, 72 + 144 = 216 students were transported by bus, and 40 + 20 = 60 students were transported by van.

Explanation:

Let's use a system of linear equations to solve this problem. We can define x as the bus capacity and y as the van capacity. Then we can write the following system of equations:

For Morel High School:

10y + 3x = 328

For Jams High School:

6x + 5y = 416

We want to find the number of students transported by bus (which is the same as the total number of students transported on buses) and the number of students transported by van (which is the same as the total number of students transported on vans).

To solve for x and y, we can use elimination. Multiplying the first equation by 2 and the second equation by 3, we get:

20y + 6x = 656

18x + 15y = 1248

Subtracting the first equation from the second, we get:

8x + 15y = 592

Solving for y in terms of x, we get:

y = (592 - 8x)/15

We can substitute this expression for y into either of the original equations to solve for x. Let's use the first equation:

10y + 3x = 328

Substituting for y, we get:

10[(592 - 8x)/15] + 3x = 328

Simplifying, we get:

592/3 - 16x/3 + 3x = 328

Combining like terms, we get:

-7x/3 = -88

Multiplying both sides by -3/7, we get:

x = 24

So the bus capacity is 24. To find the van capacity, we can substitute x = 24 into either of the equations we derived earlier. Let's use the first equation:

10y + 3x = 328

Substituting x = 24, we get:

10y + 3(24) = 328

Solving for y, we get:

y = 4

So the van capacity is 4.

Therefore, Morel High School transported 3 buses and 10 vans, which is a total of 324 = 72 students on buses and 104 = 40 students on vans. Jams High School transported 6 buses and 5 vans, which is a total of 624 = 144 students on buses and 54 = 20 students on vans. So in total, 72 + 144 = 216 students were transported by bus, and 40 + 20 = 60 students were transported by van.