Question

Jerry goes to a theme park to ride the roller coasters the theme park charges an entry fee in addition to a fee for each roller coaster ride the went below represents the total price for two different numbers of roller coaster rides.

table
#of roller coaster rides
5. total price $35
11. total price $59

what are the prices in dollars for the entry fee and for each roller coaster ride explain your answer

Answer 1

The entry fee is $15 and the price for each roller coaster ride is $4.

Step-by-step explanation:

The prices for the entry fee and each roller coaster ride can be found by solving a system of equations. Let's assign variables to the unknowns: let's say the entry fee is represented by 'E' and the price for each roller coaster ride is represented by 'R'.

From the given information, we have the following equations:

5R + E = 35 ---> Equation 1

11R + E = 59 ---> Equation 2

We can solve this system of equations by elimination or substitution. Let's use the elimination method.

Multiplying Equation 1 by -1: -5R - E = -35

Adding Equation 2 and the modified Equation 1: 11R + E + (-5R - E) = 59 + (-35)

6R = 24

Dividing both sides by 6: R = 4

Substituting the value of R into Equation 1: 5(4) + E = 35

20 + E = 35

Subtracting 20 from both sides: E = 15

Therefore, the entry fee is $15 and the price for each roller coaster ride is $4.

Answer 2

Price for roller coaster ride:x
Prices for the entry fee:y

From table: for 5 rides total price is $35: 5x+y=35
for 11 rides total price is $59: 11x+y=59

5x+y=35⇒y=35-5x
11x+y=59

y=35-5x
11x+35-5x=59⇒6x=59-35

y=35-5x
6x=24⇒x=24/6

x=4⇒y=35-5*4
y=15

Price for entry fee is $15, and for each roller coaster ride $4.