Question

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Answer 1

Answer:

8 students per van and 46 students per bus

Step-by-step explanation:

Let the number of people in each van be v.

Let the number of people in each bus be b.

High School A:

1 van and 6 buses, 284 students

1 van had 1 * v people, or simply v students.

6 buses had 6b students.

Total of 284 students.

The first equation is

6b + v = 284

Now we do the same for High School B.

1 van and 5 buses, 238 students

1 van had v students

5 buses had 5b students

Total of 238 students.

The second equation is

5b + v = 238

We have 2 equations in 2 unknowns.

6b + v = 284

5b + v = 238

Rewrite the first equation. Multiply both sides of the second equation by -1 and write it below the first equation. Then add the equations.

         6b + v = 284

(+)     -5b - v = -238

----------------------------

           b      =    46

The number of students per bus is 46.

Now we use the first equation, substitute 46 for b, and solve for v.

6b + v = 284

6(46) + v = 284

276 + v = 284

v = 8

The number of students per van is 8.

Answer: 8 students per van and 46 students per bus