Question

system by applications i think its c but just checking

Answer 1

Let v be the number of students in each Van and b be the number of students in each Bus.

If High School A filled 9 vans and 10 buses, the toal number of students is:

$9v+10b$

And this is equal to 653, so:

$9v+10b=653$

If High School B filled 9 vans and 6 buses, the toal number of students is:

$9v+6b$

And this is equal to 417, so:

$9v+6b=417$

So, the system of equations is:

$\begin{gathered} 9v+10b=653 \\ 9v+6b=417 \end{gathered}$

If we substract the second equation from the first, we will have:

$\begin{gathered} 9v+10b=653 \\ -(9v+6b=417) \\ ------------------ \\ 0v+4b=236 \\ 4b=236 \\ b=\frac{236}{4} \\ b=59 \end{gathered}$

With the value for b, we can substitute into either eqution and solve for v:

$\begin{gathered} 9v+10b=653 \\ 9v+10\cdot59=653 \\ 9v+590=653 \\ 9v=653-590 \\ 9v=63 \\ v=\frac{63}{9} \\ v=7 \end{gathered}$

Thus, the number of students in each Van is 7 and the number of students in each Bus is 59.