Sure! Let's go through these questions step by step.
### A. Cost to purchase 2 t-shirts
1. Identify the given formula:
The cost, [tex]\( c \)[/tex], for [tex]\( n \)[/tex] t-shirts is given by the equation:
[tex]\[
c = 15 + 9(n - 1)
\][/tex]
2. Substitute [tex]\( n = 2 \)[/tex] into the formula:
[tex]\[
c = 15 + 9(2 - 1)
\][/tex]
3. Simplify inside the parentheses first:
[tex]\[
c = 15 + 9(1)
\][/tex]
4. Multiply:
[tex]\[
c = 15 + 9
\][/tex]
5. Add to find the total cost:
[tex]\[
c = 24
\][/tex]
So, the cost to purchase 2 t-shirts is [tex]\(\$ 24\)[/tex].
### B. Cost to purchase 5 t-shirts
1. Substitute [tex]\( n = 5 \)[/tex] into the formula:
[tex]\[
c = 15 + 9(5 - 1)
\][/tex]
2. Simplify inside the parentheses:
[tex]\[
c = 15 + 9(4)
\][/tex]
3. Multiply:
[tex]\[
c = 15 + 36
\][/tex]
4. Add to find the total cost:
[tex]\[
c = 51
\][/tex]
So, the cost to purchase 5 t-shirts is [tex]\(\$ 51\)[/tex].
### C. Cost of each additional t-shirt after the first one
To find how much each additional t-shirt costs after the first one, we examine the given formula:
[tex]\[
c = 15 + 9(n - 1)
\][/tex]
In this formula:
- The first shirt costs [tex]\(\$ 15\)[/tex].
- The term [tex]\(\$ 9(n - 1)\)[/tex] accounts for the additional shirts.
Thus, for each additional t-shirt after the first one, the cost is:
[tex]\[
\$ 9
\][/tex]
We know this because [tex]\( 9 \)[/tex] is the coefficient of [tex]\((n-1)\)[/tex] in the given formula, representing the cost per additional t-shirt.
### Summary
- The cost to purchase 2 t-shirts is [tex]\(\$ 24\)[/tex].
- The cost to purchase 5 t-shirts is [tex]\(\$ 51\)[/tex].
- Each additional t-shirt after the first one costs [tex]\(\$ 9\)[/tex].
