System equations

Question

All 409 students in the math club went on a field trip some students rode in a van Wich holds 7 students each and some rode in busses Wich holds 60 students each. How many of each types of vehicles did they use if there were 13 vehicles total?

Answer 1

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Answer 2

Here's the substitution method:

V + B = 13 vehicles, so V = 13 - B

7V + 60B = 409 students

Substituting for V: 7(13 - B) + 60B = 409

Distributing: 91 - 7B + 60B = 409

Combining like terms and subtracting 91 from both sides; 53B = 318 Divide by 53.

B = 6 busses

So V = 13 - 6 = 7 vans

Check: 7(7) + 60(6) = 49 + 360 = 409

Answer 3