To determine the equation Jenna can use to calculate the total cost of rides at the carnival, let's break down each given equation step-by-step.
First, let's define the variables:
- [tex]\( p \)[/tex] represents the number of rides.
- [tex]\( t \)[/tex] represents the total cost.
Next, let's analyze each equation individually to see how well they fit the scenario described.
1. Equation 1: [tex]\( 6.50p + 2.50 = t \)[/tex]
- This equation suggests that the total cost [tex]\( t \)[/tex] is calculated by multiplying the number of rides [tex]\( p \)[/tex] by [tex]$6.50 and then adding a fixed amount of $[/tex]2.50.
- If we translate it, it means the cost for the rides is [tex]$6.50 for each ride plus an additional $[/tex]2.50 for some fixed expense. This doesn’t align well with the information where [tex]$2.50 is supposed to be the per-ride cost.
2. Equation 2: \( 6.50 + 2.50r = t \)
- This equation suggests that there's a fixed initial cost of $[/tex]6.50, plus [tex]$2.50 for each ride.
- In this context, \( r \) (interpreted as the number of rides) gets multiplied by the per-ride cost of $[/tex]2.50, but adding a fixed initial cost of [tex]$6.50 does not match the problem correctly. However, the symbol used should have been \( p \) as per our definitions.
3. Equation 3: \( 6.50r + 2.50 = t \)
- This equation suggests that the total cost \( t \) is calculated by multiplying the number of rides \( r \) by $[/tex]6.50 and then adding a fixed amount of [tex]$2.50.
- Similar to Equation 1, this interpretation doesn't fit well with the context where $[/tex]2.50 should be the per-ride cost not a flat fee addition.
4. Equation 4: [tex]\( 6.50 + 2.50p = t \)[/tex]
- This equation suggests a fixed initial cost of [tex]$6.50 plus $[/tex]2.50 for each ride explicitly represented by [tex]\( p \)[/tex].
- In this context, [tex]\( p \)[/tex] represents the number of rides, and $2.50 per ride directly correlates to the cost structure. Hence, it makes sense to have a fixed cost added to a variable total that's dependent on the number of rides.
Through careful analysis, the most accurate and fitting equation to use for calculating the total cost of rides at the carnival is:
[tex]\[ 6.50 + 2.50p = t \][/tex]
Therefore, Jenna should use this equation to create a table showing the total cost for different numbers of rides at the carnival. The correct equation is the fourth one:
[tex]\[ \boxed{4} \][/tex]
