Standard form word problem

Question

The senior classes at high school a and high school b planned separate trips to New York City. The senior class at high school a rented and filled 1 van and 6 buses with 372 students.high school b rented and filled 4 vans and 12 buses with 780 students . How many students can a van Carry? How many students can a bus carry?

Answer 1

Let x = number of vans

       y = number of buses

 

Then x + 6y = 372

       4x + 12y = 780

 

Multiply the first equation by -4:  -4x - 24y = -1488

                                                   4x + 12y = 780

Adding the equations, we get -12y = -708

                                                 y = 59

 

Substitute for y in the equation x + 6y = 372:

 

   x + 6(59) = 372

   x + 354 = 372

             x = 18

 

ANSWER:  each van carries 18 people and each bus can                   transport 59 people.