Answer:
A Bus could carry 30 people.
Step-by-step explanation:
Let's denote the number of students in a van as [tex]\sf v[/tex] and the number of students in a bus as [tex]\sf b[/tex].
From the information given:
For Capital High School:
- Number of vans: 14
- Number of buses: 9
- Total number of students: 354
The total number of students in vans and buses can be expressed as an equation:
[tex]\sf 14v + 9b = 354[/tex]
For Nitro High School:
- Number of vans: 7
- Number of buses: 4
- Total number of students: 162
The total number of students in vans and buses for Nitro High School can be expressed as:
[tex]\sf 7v + 4b = 162[/tex]
Now, we have a system of two equations with two unknowns:
[tex]\sf \begin{cases} 14v + 9b = 354 \\ 7v + 4b = 162 \end{cases} [/tex]
To solve for [tex]\sf b[/tex] (the number of students a bus can carry), we can use the system of equations.
One way to do this is by multiplying the second equation by 2 to make the coefficients of [tex]\sf v[/tex] in both equations match:
[tex]\sf \begin{cases} 14v + 9b = 354 \\ 14v + 8b = 324 \end{cases} [/tex]
Now, subtract the second equation from the first:
[tex]\sf \begin{aligned} (14v + 9b) - (14v + 8b) &= 354 - 324 \\ 14v +9b -14v -8b & = 30 \\ b & = 30 \end{aligned} [/tex]
So, a bus could carry 30 people.
