The state 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 9 buses with 569 students. High School B rented and filled 14 vans and 3 buses with 325 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus. The number of students that fit in each van is _ and the number of students that fit in each bus is _

The state 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 9 buses with 569 students. High School B rented and filled 14 vans and 3 buses with 325 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.

The number of students in each van = 14

The number of students in each bus = 43

Step-by-step explanation:

Let the number of students that can fill a van be v.

Let the number of students that can fill a bus be b.

The senior class at High School A rented and filled 13 vans and 9 buses with 569 students.

13 vans will have (13v) students

9 buses will have (9b) students

13v + 9b = 569

High School B rented and filled 14 vans and 3 buses with 325 students

14 vans will have (14v) students.

3 buses will have (3b) students.

14v + 3b = 325

Combining these two simultaneous equations

13v + 9b = 569

14v + 3b = 325

Solving simultaneously,

v = 14 students.

b = 43 students.

Hope this Helps!!!

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

a)(x-2)^2+(y-1)^2=9

step-by-step explanation:

(picture explains)