Algebra 1 word problems

Question

The local amusement park is a popular field trip destination. This year the senior class at High

School A and the senior class at High School B both planned trips there. The senior class at High

School A rented and filled 11 vans and 12 buses with 412 students. High School B rented and

filled 9 vans and 2 buses with 126 students. Each van and each bus carried the same number of

students. Find the number of students in each van and in each bus

Answer 1

B = no. students/bus V = no. students/bus

School A) 11 V + 12 B = 412 (No. of students in vans + no. students in buses = 412)

School B) 9 V + 2 B = 126

Need to elim one of the variables. Looks like B is best candidate.

Mult 2nd eqn by -6

11 V + 12 B = 412

-54 V - 12 B = - 756 Add:

-43 V = -344 V = -344/-43 = 8 students/van

Using 2nd equation: 9(8) + 2 B = 126 -> 2 B = 126 - 72 = 54 - > B = 27 students/bus

Substitute values back into both equations to check results.