Question

The senior classes at Snellville High and General High planned separate trips to the water park. The senior class at Snellville rented and filled 12 vans and 14 buses with 796 students. General High rented and filled 14 vans and 12 buses with 738 students. How many students would fill 2 buses and 3 vans?

Answer 1

Answer:

133 Students

Step-by-step explanation:

Let the number of student in a van=v

Let the number of student in a bus=b

The senior class at Snellville rented and filled 12 vans and 14 buses with 796 students.

Therefore: 12v+14b=796

General High rented and filled 14 vans and 12 buses with 738 students.

Therefore: 14v+12b=738

We solve the two resulting equations simultaneously

12v+14b=796

14v+12b=738

Multiply equation 1 by 12 and equation 2 by 14 to eliminate b

144v+168b=9552

196v+168b=10332

Subtract

-52v=-780

Divide both sides by -52

v=15

We substitute v=15 to obtain b in any of the equations

12v+14b=796

12(15)+14b=796

14b=796-180

14b=616

Divide both sides by 14

b=44

Therefore a bus contains 44 Students and a Van contains 15 students.

Number of Students who would fill 2 buses and 3 vans

=2b+3v

=2(44)+3(15)

=133 Students