To solve this problem, we need to follow the steps provided below in a precise and systematic manner:
1. Understand the Problem:
- We have an initial cost of \[tex]$15.50, which covers the cost for the first person.
- Each additional person incurs an extra cost of \$[/tex]12.00.
- The equation representing this total cost is [tex]\( c = 15.5 + 12f \)[/tex], where [tex]\( f \)[/tex] is the number of friends joining Gale.
2. Identify the Given Input:
- The provided input is [tex]\( f = 3 \)[/tex]. This means Gale is going to the carnival with 3 friends.
3. Substitute the Input into the Equation:
- Substitute [tex]\( f = 3 \)[/tex] into the equation [tex]\( c = 15.5 + 12f \)[/tex].
- This results in [tex]\( c = 15.5 + 12 \times 3 \)[/tex].
4. Calculate the Output:
- Compute the value inside the equation: [tex]\( 15.5 + 12 \times 3 \)[/tex].
- The product [tex]\( 12 \times 3 \)[/tex] equals 36.
- Adding 15.5 and 36 gives us 51.5.
So, if the input [tex]\( f = 3 \)[/tex], the output [tex]\( c \)[/tex] of the equation is 51.5. This means the total cost for Gale and her 3 friends to go to the carnival is \[tex]$51.50.
Now, let’s fill in the entire table based on different inputs:
\[
\begin{tabular}{|c|l|l|l|}
\hline
$[/tex]f[tex]$ & $[/tex]15.5 + 12 f[tex]$ & $[/tex]c[tex]$ & $[/tex](f, c)$ \\
\hline
3 & 15.5 + 12 \times 3 & 51.5 & (3, 51.5) \\
\hline
5 & 15.5 + 12 \times 5 & 75.5 & (5, 75.5) \\
\hline
7 & 15.5 + 12 \times 7 & 99.5 & (7, 99.5) \\
\hline
9 & 15.5 + 12 \times 9 & 123.5 & (9, 123.5) \\
\hline
\end{tabular}
\]
In conclusion, the total cost [tex]\( c \)[/tex] for Gale and her friends can be calculated accurately using the equation [tex]\( c = 15.5 + 12f \)[/tex].
