A group of friends wants to go to the movies. If the friends take 3 vans and 5 cars, they can transport 38 people. If they take 2 vans and 4 cars, they can transport 28 people. Define variables and write a system of equations to find out how many people a van can hold and how many people a car can hold.

3v +  c = 22  ---> c = 22 - 3v

2v + 4c = 28 ---> 2v + 4(22 - 3v) = 28

                         2v + 88 - 12v = 28

                       -10v + 88 = 28

                               - 88  - 88

                        - 10v = - 60

                              v = 6 students

Step-by-step explanation:

This problem can be solved by using the rules of system of equations. You have two situations: 1) when 3 vans and  1 car can transport 22 student; 2) when 2 vans and 4 cars can transport 28 students. Let's name students in the van V; students in the car - C.  Now think this way: in first case 3 vans can take V students (3V) and 1 car - C students (1C).Let's write the equation for this case: 3V+ 1C = 22

Think the same way about the second case: 2 vans can take V students (2V), 4 cars - 4C students. Total number of students in the second case - 28. Let's write the equation for this case: 2V + 4C = 28.

Now you have two equations of the system, write them one under another and solve by SUBSTITUTION method.

3V+ 1C = 22             1c = -3V + 22   Substitute 1C by its equivalent (-3V + 22) in the green system:                                                                                                                                            2V + 4C = 28.          2v + 4(-3V +22) = 28

                                2v  - 12v +88= 28  Combine  Vs together:

                              -10v         + 88 = 28

                                               - 88 - 88

                               - 10v = - 60

                                  v = 6 students

c.

step-by-step explanation:

she should of added 9^2 and 12^2. that is because it is a^2+b^2=c^2. c^2 is the hypotenuse and should always be bigger than the other two numbers. which is why she should of added 9 squared and 12 squared together instead of 15 squared.

c. 1,233 miles