College

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

Answer :

To solve this problem, we'll find out which equation correctly represents the situation where Will purchased 7 neckties, each at a discounted price.

Let's break down the information given:

1. Will bought 7 neckties.
2. Each necktie costs \[tex]$8 less than its full price.
3. The total amount Will paid for the 7 neckties was \$[/tex]147.

Now, we want to find the full price of each necktie, which we’ll represent by [tex]\( f \)[/tex].

Step-by-step Solution:

1. Understand the Prices:
- The full price of each necktie is [tex]\( f \)[/tex].
- During the sale, each necktie was sold for $8 less than its full price. So the sale price of one necktie would be [tex]\( f - 8 \)[/tex].

2. Set Up the Equation:
Since Will bought 7 neckties at the sale price, the total amount he paid is calculated by multiplying the number of neckties by the sale price of each necktie:
[tex]\[
7 \times (f - 8) = 147
\][/tex]

3. Interpret the Equation:
The equation [tex]\( 7(f - 8) = 147 \)[/tex] effectively states that when you buy 7 neckties at a price of [tex]\( (f - 8) \)[/tex] dollars each, the total should be 147 dollars.

By understanding each step and setting up the equation [tex]\( 7(f - 8) = 147 \)[/tex], you'll be able to find the full price [tex]\( f \)[/tex] when solving this equation. This equation correctly represents the situation described in the problem.