Question

Two high schools are planning their Senior trips to Washington DC. High School A rented 2 vans and 6 busses to carry all 366 seniors. High School B rented 5 vans and 4 busses to carry all 277 seniors. How many students can a van carry? . How many students can a bus carry?

Answer 1

Van = 9

Bus = 58

Explanation:

Based on the given,

School A = 2 Vans + 6 Busses = 366 Seniors

School B = 5 Vans + 4 Busses = 277 Seniors.

Question to answer:

How many students can a van carry?

How many students can a bus carry?

Solution:

Let's put it into equations.

Let,

x = Vans [x represent the number of Vans]

y = Busses [y represent the number of Busses]

School A equation: 2x + 6y = 366

School B equation: 5x + 4y = 277

Now since we have the equations we can start solving;

2x + 6y = 366

5x + 4y = 277

Let's use substitution method.

Substitution method is basically substitute one equation to the other one.

Before we do that we have to get y by itself.

Thus,

5x + 4y = 277

5x - 5x + 4y = 277 - 5x [Subtract 5x and put it to the other side]

4y = -5x + 277

4y/4 = -5x/4 + 277/4 [Divide all side by 4]

y = -5/4x + 69.25

Now substitute it in:

2x + 6(5/4x + 69.25) = 366

-11 = -99

x = 9

Now we know that x = 9, we can use top or bottom equation and substitute to find x.

Or we can also use;

y = -5/4x + 69.25

y = -5/4(9) + 69.25

y = 58.

As a result,

A van can carry 9 students and a bus can carry 58 students.

To check answer:

2x + 6y = 366

2(9) + 6(58) = 366

18 + 348 = 366

366 = 366

5x + 4y = 277

5(9) + 4(58) = 277

45 + 232 = 277

277 = 277

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