Answered

The senior classes at West High School and East High School planned separate trips to Medicine Hat, AB. The senior class at West High School rented and filled 4 vans and 8 buses with 488 students. East High School rented 1 van and 9 buses and filled them with 500 students.

Let [tex]v[/tex] be the number of students a van will carry.
Let [tex]b[/tex] be the number of students a bus will carry.

The system of equations that represents this situation is:
[tex]\[
\begin{array}{c}
4v + 8b = 488 \\
v + 9b = 500
\end{array}
\][/tex]

Written Response:
1. Algebraically determine the number of students each type of vehicle will carry. (2 marks)



Answer :

GinnyAnswer
So, to find the number of students each type of vehicle will carry, we are given the system of equations:

[tex]\[ \begin{cases} 4v + 8b = 488 \\ v + 9b = 500 \end{cases} \][/tex]

We need to determine the values of [tex]\( v \)[/tex] and [tex]\( b \)[/tex]. Here is the step-by-step solution:

1. Solve the second equation for [tex]\( v \)[/tex]:
[tex]\[ v + 9b = 500 \][/tex]
[tex]\[ v = 500 - 9b \][/tex]

2. Substitute [tex]\( v = 500 - 9b \)[/tex] into the first equation:
[tex]\[ 4v + 8b = 488 \][/tex]
[tex]\[ 4(500 - 9b) + 8b = 488 \][/tex]
Simplify the expression:
[tex]\[ 2000 - 36b + 8b = 488 \][/tex]
Combine like terms:
[tex]\[ 2000 - 28b = 488 \][/tex]

3. Isolate the variable [tex]\( b \)[/tex]:
[tex]\[ 2000 - 488 = 28b \][/tex]
[tex]\[ 1512 = 28b \][/tex]
Divide both sides by 28:
[tex]\[ b = \frac{1512}{28} \][/tex]
[tex]\[ b = 54 \][/tex]

4. Substitute [tex]\( b = 54 \)[/tex] back into the equation [tex]\( v = 500 - 9b \)[/tex]:
[tex]\[ v = 500 - 9(54) \][/tex]
[tex]\[ v = 500 - 486 \][/tex]
[tex]\[ v = 14 \][/tex]

Therefore, the number of students each type of vehicle will carry is:
- [tex]\( v = 14 \)[/tex] students per van
- [tex]\( b = 54 \)[/tex] students per bus

So, the final answer is:
- Each van will carry 14 students.
- Each bus will carry 54 students.

Other Questions