Need help with this math problem.

Question

MME rented and filled 2 vans and 2 buses with 60 students. MMW rented and filled 4 vans and 1 bus with 54 students. Every van had the same number of students in it as did the buses.

Number of students in each van:

Number of students in each bus:

Answer 1

Let V = #students in each van

B = #students in each bus

For MME this is the situation:

2V + 2B = 60 (there are two vans and two buses)

If that is true then so is:

V + B = 30 (divide every term by 2)

For MMW this is the situation:

4V + 1B = 54 (four vans and one bus)

Likely the easiest way to solve this system is to isolate B in the first equation, then substitute into the 2nd equation:

If

V + B = 30, then B = 30 - V

Substituting:

4V + 1B = 54

4V + 1(30 - V) = 54

4V + 30 - V = 54

3V = 24

V = 8

If V = 8, then B = 30 - 8 = 22.

So each van holds 8 students and each bus holds 22 students.

MME: 2(8) + 2(22) = 16 + 44 = 60

MMW: 4(8) + 1(22) = 32 + 22 = 54

Another way to solve the system is the elimination method:

4V + B = 54

V + B = 30

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3V = 24 (subtract bottom equation from top)

V = 8