A class used vans and buses to go on a field trip. They used 15 vehicles to go on a trip. Each van holds 9 students and each bus holds 30 students. If 282 students went on the trip then how many of each type of vehicle did the class use?

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alinakincsem alinakincsem · Answer 1 · 2018-11-15T20:22:12+01:00

Answer:

7 buses and 8 vans

Step-by-step explanation:

We know that 292 students went on a trip. Each van holds 9 students and each bus holds 30 students and total 15 vehicles were used.

Assuming the vans as [tex]v[/tex] and buses as [tex]b[/tex], we can make the following equations with the help of the given data:

[tex]v+b=15[/tex] --- (1)

[tex]9v+30b = 282[/tex] --- (2)

Using the substitution method:

[tex]v=15-b[/tex]

Putting this value of [tex]v[/tex] in equation 2:

[tex]9(15-b)+30b=282[/tex]

[tex]135-9b+30b=282[/tex]

[tex]21b=282-135[/tex]

[tex]21b=147[/tex]

[tex]b=7[/tex]

so [tex]v=15-7=8[/tex]

Therefore, 7 buses and 8 vans were used on the trip by the class.