Question

one high school rented and filled 2 vans and 8 buses with 218 students. another high school used 9 vans and 5 buses with 206 students. each bus and van seats the same number of students. how many students can the bus carry? how many students can the van carry?

Explanation:

Let \( x \) be the number of students a van can carry and \( y \) be the number of students a bus can carry.

Step1: Set up equations from the problem

From the first high school: \( 2x + 8y = 218 \)
From the second high school: \( 9x + 5y = 206 \)

Step2: Solve the system of equations. First, multiply the first equation by 9 and the second by 2 to eliminate \( x \)

\( 18x + 72y = 1962 \) (from first equation * 9)
\( 18x + 10y = 412 \) (from second equation * 2)

Step3: Subtract the second new equation from the first to solve for \( y \)

\( (18x + 72y)-(18x + 10y)=1962 - 412 \)
\( 62y = 1550 \)
\( y=\frac{1550}{62}=25 \)

Step4: Substitute \( y = 25 \) into the first original equation to solve for \( x \)

\( 2x+8\times25 = 218 \)
\( 2x+200 = 218 \)
\( 2x=218 - 200=18 \)
\( x = 9 \)

Answer:

A van can carry 9 students and a bus can carry 25 students.