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Ed is booking a hotel room for his vacation. If he stays for 77 nights, the hotel will give him a $280\$280 discount. He notices that the amount he would pay for 77 nights with the discount is the same as the amount he would pay for 55 nights without the discount.\newlineWhich equation can you use to find pp, the full price of the hotel room per night?\newlineChoices:\newline(A) 7p=2805p7p = 280 - 5p\newline(B) 7p280=5p7p - 280 = 5p\newlineWhat is the full price of the hotel room per night?\newline____ $\$

Full solution

Q. Ed is booking a hotel room for his vacation. If he stays for 77 nights, the hotel will give him a $280\$280 discount. He notices that the amount he would pay for 77 nights with the discount is the same as the amount he would pay for 55 nights without the discount.\newlineWhich equation can you use to find pp, the full price of the hotel room per night?\newlineChoices:\newline(A) 7p=2805p7p = 280 - 5p\newline(B) 7p280=5p7p - 280 = 5p\newlineWhat is the full price of the hotel room per night?\newline____ $\$
  1. Set Up Equation: Let's set up the equation based on the information given. We know that the price for 77 nights with a $280\$280 discount is the same as the price for 55 nights without the discount. This can be written as:\newline77 nights * (full price per night) - $280\$280 discount = 55 nights * (full price per night)\newlineSo the equation is:\newline7p280=5p7p - 280 = 5p
  2. Isolate pp: Now we need to solve for pp. To do this, we should isolate pp on one side of the equation. We can start by subtracting 5p5p from both sides to get the pp terms on one side:\newline7p5p280=5p5p7p - 5p - 280 = 5p - 5p\newlineThis simplifies to:\newline2p280=02p - 280 = 0
  3. Add 280280: Next, we add 280280 to both sides to isolate the term with pp: \newline2p280+280=0+2802p - 280 + 280 = 0 + 280\newlineThis gives us:\newline2p=2802p = 280
  4. Divide by 22: Finally, we divide both sides by 22 to solve for pp:2p2=2802\frac{2p}{2} = \frac{280}{2}This results in:p=140p = 140

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