Question

1. the water 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 7 vans and 6 buses with 247 students. high school b rented and filled 14 vans and 4 busses with 230 students. every van had the same number of students in it as did the buses. find the number of students in each van and 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

From High School A: \( 7v + 6b = 247 \)
From High School B: \( 14v + 4b = 230 \)

Step3: Simplify the Second Equation

Divide the second equation by 2: \( 7v + 2b = 115 \)

Step4: Subtract Equations

Subtract the simplified second equation from the first equation:
\( (7v + 6b) - (7v + 2b) = 247 - 115 \)
\( 4b = 132 \)

Step5: Solve for \( b \)

\( b = \frac{132}{4} = 33 \)

Step6: Substitute \( b \) into Simplified Equation

Substitute \( b = 33 \) into \( 7v + 2b = 115 \):
\( 7v + 2(33) = 115 \)
\( 7v + 66 = 115 \)
\( 7v = 115 - 66 = 49 \)

Step7: Solve for \( v \)

\( v = \frac{49}{7} = 7 \)

Answer:

Number of students in each van: \( 7 \), Number of students in each bus: \( 33 \)