To determine the correct answer, let's break down the problem step-by-step.
1. Identify the original price of the television:
- The original price of the television is given by [tex]\( p \)[/tex].
- In this scenario, [tex]\( p = \$1,500 \)[/tex].
2. Discount offered:
- The television is sold at [tex]\( 80\% \)[/tex] of its original price.
- [tex]\( 80\% \)[/tex] can be expressed as [tex]\( \frac{80}{100} \)[/tex].
3. Calculate the discounted price of the television:
- To find the discounted price, multiply the original price [tex]\( p \)[/tex] by [tex]\( \frac{80}{100} \)[/tex].
- [tex]\[ \text{Discounted Price} = p \times \frac{80}{100} \][/tex]
4. Membership fee:
- To get the discounted price, the customer has to buy a store membership which costs [tex]\( \$100 \)[/tex].
5. Calculate the total cost including the membership fee:
- Add the membership fee to the discounted price.
- [tex]\[ \text{Total Cost} = \left(p \times \frac{80}{100}\right) + 100 \][/tex]
Let's apply these steps to find out how much a [tex]$1,500 television will cost including the membership fee:
1. Original price (\( p \)):
- \( p = \$[/tex]1,500 \).
2. Calculate the discounted price:
- [tex]\[ \text{Discounted Price} = 1500 \times \frac{80}{100} = 1500 \times 0.80 = 1200 \][/tex]
3. Add the membership fee:
- [tex]\[ \text{Total Cost} = 1200 + 100 = 1300 \][/tex]
So, the complete expression representing the amount that a new customer will have to pay is:
[tex]\[ \left(p \times \frac{80}{100}\right) + 100 \][/tex]
And for a [tex]$1,500 television, the total cost, including the membership fee, would be $[/tex]1,300.
Therefore, the correct answer is:
C. The expression is [tex]\(\left(p \times \frac{80}{100}\right)+100\)[/tex], and the cost is \$1,300.
