Question

A state park charges an entrance fee based on the number of people in a vehicle. A car containing 2 people is charged $14, a car containing 4 people is charged $20, and a van containing 8 people is charged $32. So how much is a bus containing 30 people be charged

Answer 1

Answer:

Therefore $98 is be charged a bus containing 30 people.

Step-by-step explanation:

Given that,

A state park charges an entrance fee based on the number of people in vehicle.

Let the entry fee for the vehicle be E and entry fee for each person be x.

Then

C= E+(P×x)

C= Total charge in $

E= entry fee for a vehicle

P=No. of person

x= Entry charge per person.

Given A car containing 2 people charged $14

C=$14, P=2

∴14= E+(2× x)

⇒E+2x=14.....(1)

Again A car containing 4 people charged $20

C=$20, P=4

∴20= E+(4× x)

⇒E+4x=20.....(2)

Subtract (1) from (2), we get

E+4x-(E+2x)= 20-14

⇒E+4x-E-2x=6

⇒2x=6

⇒x=3

Putting the value of x in equation (1)

E+(2×3)=14

⇒E=14-6

⇒E=8

Therefore E=$8 and x=$3

Next we check whether our assumption is correct or wrong. Putting the value of E and x for third case

Here P= 8

Therefore C= E+(P×x)

                    = 8+(8× 3)

                    =8+24

                   =$32

Therefore our assumption is correct.

Now C=? , P= 30

The charged for the 30 people is

C= $[8+(30×3)]

  =$[8+90]

 =$98

Therefore $98 is be charged a bus containing 30 people.