To solve this problem, we need to represent the total cost of attending the carnival and taking a number of rides, and then relate this total cost to the amount of money you have, which is [tex]$50.
1. Admission Cost: The cost of admission to the carnival is \$[/tex]6.
2. Ride Cost: Each ride at the carnival costs \[tex]$2.50.
Let's denote \( r \) as the number of rides you want to take.
3. Total Cost: The total cost \( C \) of attending the carnival and taking \( r \) rides can be expressed as:
\[
C = 6 + 2.5r
\]
This equation combines the flat admission fee of \$[/tex]6 with the variable cost that increases with each ride you take.
4. Budget Constraint: You have a total of \[tex]$50 to spend. Therefore, the total cost should not exceed \$[/tex]50. This can be mathematically represented by the inequality:
[tex]\[
6 + 2.5r \leq 50
\][/tex]
We have the inequality that represents the situation:
[tex]\[
2.5r + 6 \leq 50
\][/tex]
Now let's look at the options provided:
A) [tex]\(2.5r < 50\)[/tex]
B) [tex]\(2.5r + 6 \leq 50\)[/tex]
C) [tex]\(2.5r + 6 > 50\)[/tex]
D) [tex]\(6r + 2.5 \geq 50\)[/tex]
Option B, [tex]\(2.5r + 6 \leq 50\)[/tex], is the correct representation of our inequality.
To further understand it:
- Subtract the cost of admission from your total money to find out how much is left for rides:
[tex]\[
50 - 6 = 44
\][/tex]
- Calculate the maximum number of rides you can take by dividing the remaining money by the cost per ride:
[tex]\[
\frac{44}{2.5} = 17.6
\][/tex]
Therefore, the correct inequality that models this situation is: [tex]\(\boxed{2.5r + 6 \leq 50}\)[/tex], which corresponds to option B.
