Question

If the senior class at High School A filled 12 vans and 8 buses with 420 students, and the senior class at High School B filled 6 vans and 13 buses with 588 students, how many students can a van carry? How many students can a bus carry?

Answer 1

By setting up a system of equations and using elimination, we find that a van can carry 7 students and a bus can carry 42 students.

Step-by-step explanation:

To solve for the number of students that can fit in a van and a bus for High School A and B, we can set up a system of equations. Let v be the number of students that a van can carry and b be the number of students that a bus can carry.

• For High School A: 12v + 8b = 420
• For High School B: 6v + 13b = 588

We can solve this system using either substitution or elimination. Let's use elimination by multiplying the first equation by 6 and the second equation by 12 to make the coefficients of v the same:

• (6)(12v + 8b) = (6)(420)
• (12)(6v + 13b) = (12)(588)

This becomes:

• 72v + 48b = 2520
• 72v + 156b = 7056

Now we subtract the first new equation from the second:

• 72v + 156b - (72v + 48b) = 7056 - 2520

Which simplifies to:

• 108b = 4536

Dividing by 108 gives us the number of students a bus can carry:

• b = 42

We can substitute b = 42 back into the first original equation:

• 12v + 8(42) = 420

Which simplifies to:

• 12v + 336 = 420

Subtracting 336 from 420 gives us:

• 12v = 84

Dividing by 12 gives us the number of students a van can carry:

• v = 7

So, a van can carry 7 students and a bus can carry 42 students.