Question

29 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 table below represents the total price for two different numbers of roller coaster rides. (a) theme park number of roller coaster rides total price 5 $35 11 $59 part a what are the prices, in dollars, for the entry fee and for each roller coaster ride? entry fee $ 15 one roller coaster ride $ 4

Explanation:

Step1: Define variables

Let \( e \) be the entry fee (in dollars) and \( r \) be the cost per roller coaster ride (in dollars). The total cost \( C \) for \( n \) rides is \( C = e + nr \).

For \( n = 5 \), \( C = 35 \), so \( 35 = e + 5r \).
For \( n = 11 \), \( C = 59 \), so \( 59 = e + 11r \).

Step2: Subtract the two equations

Subtract the first equation from the second:
\( (e + 11r) - (e + 5r) = 59 - 35 \)
Simplify: \( 6r = 24 \)
Solve for \( r \): \( r = \frac{24}{6} = 4 \).

Step3: Find the entry fee

Substitute \( r = 4 \) into \( 35 = e + 5r \):
\( 35 = e + 5(4) \)
\( 35 = e + 20 \)
Solve for \( e \): \( e = 35 - 20 = 15 \).

Answer:

Entry fee: \(\$15\), One roller coaster ride: \(\$4\)