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For a trip, one high school rented and filled 5 vans and 6 buses with 187 students. Another high school instead fit its 176 students into 2 vans and 7 buses. With each bus and van seating the same number of students, how many students can a bus carry? How many students can a van carry?

Respuesta :

Answer:

A bus can carry 22 students and a van can carry 11 students.

Step-by-step explanation:

Let the number of students bus can carry be 'b'.

Let the number of students van can carry be 'v'.

Given:

One High school:

Number of bus = 6

Number of vans = 5

Number of students = 187

So we can say that;

Number of bus multiplied by number of students bus can carry plus Number of vans multiplied by number of students van can carry is equal to Number of students.

framing in equation form we get;

[tex]6b+5v=187[/tex]  ⇒ Equation 1

Also Given:

One High school:

Number of bus = 7

Number of vans = 2

Number of students = 176

So we can say that;

Number of bus multiplied by number of students bus can carry plus Number of vans multiplied by number of students van can carry is equal to Number of students.

framing in equation form we get;

[tex]7b+2v=176[/tex]  ⇒ Equation 2

Now multiplying equation 2 by 5  we get;

[tex]5(7b+2v)=5\times176[/tex]

[tex]35b+10v=880[/tex] ⇒ Equation 3

Now multiplying Equation 1 by 2 we get;

[tex]2(6b+5v)=187\times2[/tex]

[tex]12b+10v=374[/tex]  ⇒ Equation 4

Subtracting equation 4 from equation 3 we get;

[tex]35b+10v-(12b+10v)=880-374\\\\35b+10v-12b-10v= 506\\\\23b =506\\\\b =\frac{506}{23} =22\ students[/tex]

Substituting value of b in equation 2 we get;

[tex]7b+2v =176\\\\7\times 22+2v =176\\\\154+2v=176\\\\2v=176-154\\\\2v =22\\\\v =\frac{22}{2}=11\ students[/tex]

Hence A bus can carry 22 students and a van can carry 11 students.

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