Question

1. the senior classes at high school a and high school b planned separate trips to the state fair. the senior class at high school a rented and filled 7 vans and 2 buses with 124 students. high school b rented and filled 7 vans and 1 bus with 90 students. each van and each bus carried the same number of students. find the number of students in each van and in each bus.

Explanation:

Step1: Define variables

Let \( v \) be the number of students in each van and \( b \) be the number of students in each bus.

Step2: Set up equations

For High School A: \( 7v + 2b = 124 \)
For High School B: \( 7v + b = 90 \)

Step3: Subtract the second equation from the first

\( (7v + 2b) - (7v + b) = 124 - 90 \)
\( 7v + 2b - 7v - b = 34 \)
\( b = 34 \)

Step4: Substitute \( b = 34 \) into the second equation

\( 7v + 34 = 90 \)
\( 7v = 90 - 34 \)
\( 7v = 56 \)
\( v = \frac{56}{7} = 8 \)

Answer:

The number of students in each van is 8 and in each bus is 34.