Please help me with this problem!

Question

Yellowstone National 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 High School A rented and filled 13 vans and 7 buses with 536 students. High School B rented and filled 3 vans and 14 buses with 681 students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many students can a bus carry?

Answer 1

Let n = number of buses and m = number of van. Then we can write two equations as follows:

For HS A 13 m + 7 n = 536 For HS B 3 m + 14 n = 681

If we multiply the A equation on both sides by - 2 and then add both equations together the n terms cancel leaving us with

23 m = 391 Solving, we get m = 17

Plug 17 into either of the original two equations and solve for n getting n = 45

Answer 2

Let V = # of Vans

Let B = # of Buses

Then the two equations are:

13V + 7B = 536

3V + 14B = 681

Solving these equations in whatever manner you choose,

The answers are a Van holds 17 students, and a Bus holds 45 students.