Write a System of Equations to solve the following problem: The county fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 13 vans and 2 buses with 211 students. High School B rented and filled 4 vans

and 4 buses with 268 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.

#students each VAN can carry:

#students each BUS can carry:

each van carries 7 students

each bus carries 60 students

Step-by-step explanation:

let v = # students in a van

let b = # students in a bus

system of equations:

13v + 2b = 211

4v + 4b = 268

I multiplied the 1st equation by -2 to eliminate the 'b' terms

 -26v - 4b = -422

+ 4v  + 4b = 268

-22v = -154

v = 7

substitute  '7' for 'v':

4(7) + 4b = 268

28 + 4b = 268

4b = 240

b = 60

13v + 2b = 211

4v + 4b = 268

#students each VAN can carry:   7

#students each BUS can carry: 60

Step-by-step explanation:

Let v = number of students in each van.

Let b = number of students in each bus.

High School A:

13v + 2b = 211

High School B:

4v + 4b = 268

The system of equations is

13v + 2b = 211

4v + 4b = 268

We will solve this system of equation with the addition method.

Write the first equation as it is. Divide both sides of the first equation by 2 and write it below the first equation. Then add the equations.

        13v + 2b = 211

(+)     -2v - 2b = -134

        11v         = 77

Divide both sides by 11.

v = 7

Substitute 7 for v in the first original equation and solve for b.

13v + 2b = 211

13(7) + 2b = 211

91 + 2b = 211

Subtract 91 from both sides.

2b = 120

Divide both sides by 2.

b = 60

13v + 2b = 211

4v + 4b = 268

#students each VAN can carry:   7

#students each BUS can carry: 60

9 x 8 divided by (5-3)=36

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.