Question

ed is booking a hotel room for his vacation. if he stays for 7 nights, the hotel will give him a $280 discount. he notices that the amount he would pay for 7 nights with the discount is the same as the amount he would pay for 5 nights without the discount. which equation can you use to find p, the full price of the hotel room per night? 7p = 280 - 5p 7p - 280 = 5p what is the full price of the hotel room per night? $

Explanation:

Part 1: Finding the Correct Equation

Step1: Analyze 7 - night cost

The full price for 7 nights is \(7p\), and with a \(\$280\) discount, the cost becomes \(7p - 280\).

Step2: Analyze 5 - night cost

The full price for 5 nights is \(5p\) (no discount).

Step3: Set up the equation

Since the cost for 7 nights with discount equals the cost for 5 nights without discount, we have \(7p - 280 = 5p\).

Part 2: Solving for \(p\)

Step1: Isolate \(p\) terms

Start with \(7p - 280 = 5p\). Subtract \(5p\) from both sides: \(7p - 5p - 280 = 0\), which simplifies to \(2p - 280 = 0\).

Step2: Solve for \(p\)

Add 280 to both sides: \(2p = 280\). Then divide both sides by 2: \(p=\frac{280}{2}\).

Step3: Calculate the value

\(\frac{280}{2}=140\).

Answer:

(Equation): \(7p - 280 = 5p\)