Question

the local amusement park is a popular field trip destination. this year the senior class at high school a and the senior class at high school b both planned trips there. the senior class at high school a rented and filled 16 vans and 8 buses with 752 students. high school b rented and filled 5 vans and 5 buses with 380 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

For School A: $16v + 8b = 752$
For School B: $5v + 5b = 380$

Step3: Simplify School B equation

Divide by 5: $v + b = 76$, so $v = 76 - b$

Step4: Substitute into School A equation

$16(76 - b) + 8b = 752$
Expand: $1216 - 16b + 8b = 752$
Simplify: $1216 - 8b = 752$

Step5: Solve for $b$

$-8b = 752 - 1216$
$-8b = -464$
$b = \frac{-464}{-8} = 58$

Step6: Solve for $v$

$v = 76 - 58 = 18$

Answer:

A van can carry 18 students, and a bus can carry 58 students.