Question

10) The senior classes at High School A and High School B planned separate trips to New York City.The senior class at High School A rented and filled 11 vans and 9 buses with 352 students. HighSchool B rented and filled 11 vans and 3 buses with 220 students. Each van and each bus carried thesame number of students. Find the number of students in each van and in each bus.A) Van: 14, Bus: 22 B) Van: 16, Bus: 35 C) Van: 6, Bus: 24Van: 22, Bus: 14

Answer 1

Solution:

$\begin{gathered} \text{Let the number of students in vans be represented by v} \\ \text{Let the number of students in buses be represented by b} \end{gathered}$

Given:

$\begin{gathered} \text{High school A filled 11 vans and 9 buses with 352 students. This means;} \\ 11v+9b=352\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(1) \\ \\ \text{High school B filled 11 cans and 3 buses with 220 students. This means;} \\ 11v+3b=220\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(2) \end{gathered}$

Solving both equations simultaneously by subtracting equation (2) from equation (1);

$\begin{gathered} \text{Equation (1)-(2);} \\ 11v-11v+9b-3b=352-220 \\ 6b=132 \\ \text{Dividing both sides by 6;} \\ b=\frac{132}{6} \\ b=22 \\ \\ \\ \text{Substituting b in equation (2) to get the value of v;} \\ 11v+3b=220 \\ 11v+3(22)=220 \\ 11v+66=220 \\ 11v=220-66 \\ 11v=154 \\ \text{Dividing both sides by 11,} \\ v=\frac{154}{11} \\ v=14 \end{gathered}$

Therefore,

The number of students in each van is 14 students

The number of students in each bus is 22 students.

OPTION A is the correct answer.