To find the cost, [tex]\( c \)[/tex], for [tex]\( n \)[/tex] t-shirts in an apparel shop where the first t-shirt costs [tex]$15 and each additional t-shirt costs $[/tex]9 less, we are given the expression:
[tex]\[ c = 15 + 9(n - 1) \][/tex]
Let’s break down the steps to understand how to calculate the total cost [tex]\( c \)[/tex] for [tex]\( n \)[/tex] t-shirts.
1. Identify the cost of the initial t-shirt: The first t-shirt is given to cost [tex]$15.
2. Determine the cost for additional t-shirts: Each additional t-shirt costs $[/tex]9 less than the first t-shirt. This means that additional t-shirts cost [tex]$9 each.
3. Set up the equation: The cost for \( n \) t-shirts is given by the function \( c = 15 + 9(n - 1) \).
- Here, \( n - 1 \) represents the number of additional t-shirts beyond the first one.
- Therefore, we add $[/tex]9 for each of these additional t-shirts to the base cost of [tex]$15 for the first t-shirt.
Let's apply this formula with an example to see it in action:
Assume we want to find the cost for \( n = 10 \) t-shirts.
\[ c = 15 + 9(10 - 1) \]
4. Calculate the term inside the parenthesis:
\[ 10 - 1 = 9 \]
5. Compute the multiplication:
\[ 9 \times 9 = 81 \]
6. Add the initial cost to the additional cost:
\[ c = 15 + 81 \]
7. Perform the addition:
\[ c = 96 \]
So, the total cost for 10 t-shirts is \( \boxed{96} \).
Thus, following these steps, we find that the cost for buying 10 t-shirts is $[/tex]96.
