At Trendy Tailor Boutique's annual end-of-season sale, every necktie in the shop is marked down. Will purchased 7 neckties during the sale. Each necktie cost [tex]$8[/tex] less than its full price. He paid a total of [tex]$147[/tex].

Which equation can you use to find [tex]f[/tex], the cost of each necktie at full price?

A. [tex]7f - 8 = 147[/tex]
B. [tex]8f - 7 = 147[/tex]
C. [tex]7(f - 8) = 147[/tex]
D. [tex]8(f - 7) = 147[/tex]

Sure! Let's work through this problem step-by-step to find the equation that represents the given situation.

1. Identify the Variables:
- Let [tex]$ f $[/tex] be the full price of each necktie.

2. Mark Down Information:
- Each necktie costs \[tex]$8 less than its full price during the sale.

3. Calculate the Sale Price of a Necktie:
- The sale price of each necktie is $ f - 8 $ dollars.

4. Total Cost for 7 Neckties:
- Will bought 7 neckties, so the total cost can be represented by the equation:
\[
7 \times (f - 8)
\]

5. Given Total Expense:
- Will paid a total of $[/tex]147. Therefore, the equation for the total cost is:
[tex]\[
7 \times (f - 8) = 147
\][/tex]

Comparing the options provided:
- [tex]$ 7f - 8 = 147 $[/tex]
- [tex]$ 8f - 7 = 147 $[/tex]
- [tex]$ 7(f - 8) = 147 $[/tex]
- [tex]$ 8(f - 7) = 147 $[/tex]

We can see that the correct equation that represents the problem is:
[tex]\[
7(f - 8) = 147
\][/tex]

Therefore, the equation you can use to find [tex]$ f $[/tex], the cost of each necktie at full price, is:
[tex]\[
7(f - 8) = 147
\][/tex]