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.
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.
