Question

1. the senior classes at high school a and high school b planned trips to new york city. the senior class at high school a rented and filled 1 van and 6 buses with 372 students. high school b rented and filled 6 vans and 12 buses with 780 students. each van and each bus carried the same number of students. how many students can a van carry? how many students can a bus carry?

Explanation:

Step1: Define variables

Let $v$ = students per van, $b$ = students per bus.

Step2: Set up equations

High School A: $v + 6b = 372$
High School B: $4v + 12b = 780$

Step3: Simplify second equation

Divide by 4: $v + 3b = 195$

Step4: Subtract equations

$(v + 6b) - (v + 3b) = 372 - 195$
$3b = 177$

Step5: Solve for $b$

$b = \frac{177}{3} = 59$

Step6: Solve for $v$

Substitute $b=59$ into $v + 3b = 195$:
$v + 3(59) = 195$
$v + 177 = 195$
$v = 195 - 177 = 18$

Answer:

A van can carry 18 students, and a bus can carry 59 students.