Answer:
23 school vans and 19 school buses
Step-by-step explanation:
Let x be the number of school vans and y be the number of school buses needed.
1. There are a total of 42 vehicles, so
[tex]x+y=42[/tex]
2. Students will ride in school vans which carry 8 passengers, so in x vans there will be [tex]8x[/tex] passengers and on schools buses which carry 40 passengers, so in y buses there will be [tex]40y[/tex] passengers. There are 944 students going. Therefore,
[tex]8x+40y=944[/tex]
a. You get the system of two equations:
[tex]\left\{\begin{array}{l}x+y=42\\ \\8x+40y=944\end{array}\right.[/tex]
b. From the first equation:
[tex]x=42-y[/tex]
Substitute it into the second equation:
[tex]8(42-y)+40y=944[/tex]
Divide this equation by 8:
[tex]42-y+5y=118\\ \\42+4y=118\\ \\4y=118-42\\ \\4y=76\\ \\y=19\\ \\x=42-19=23[/tex]
23 school vans and 19 school buses
