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Meg wants to buy paint and a roller to repaint her bedroom. She could buy a gallon of paint from the sales bin for 30%30\% off, then pay 13.5013.50 $\$ for the roller. Alternatively, if she pays full price for a gallon of paint, she would get a roller for free. After considering her options, she realizes she would pay the same amount either way.\newlineWhich equation can you use to find pp, the full price of one gallon of paint?\newlineChoices:\newline(A)0.7p+13.5=p0.7p + 13.5 = p\newline(B)0.3p+13.5=p0.3p + 13.5 = p\newlineWhat is the full price of one gallon of paint?\newline___\_\_\_ $\$

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Q. Meg wants to buy paint and a roller to repaint her bedroom. She could buy a gallon of paint from the sales bin for 30%30\% off, then pay 13.5013.50 $\$ for the roller. Alternatively, if she pays full price for a gallon of paint, she would get a roller for free. After considering her options, she realizes she would pay the same amount either way.\newlineWhich equation can you use to find pp, the full price of one gallon of paint?\newlineChoices:\newline(A)0.7p+13.5=p0.7p + 13.5 = p\newline(B)0.3p+13.5=p0.3p + 13.5 = p\newlineWhat is the full price of one gallon of paint?\newline___\_\_\_ $\$
  1. Set Up Equation: Meg is considering two options for buying paint and a roller. If she buys the paint at 30%30\% off, she pays 13.5013.50 (\$) for the roller. If she pays full price for the paint, the roller is free. Since the total cost is the same in both scenarios, we can set up an equation where the cost of the discounted paint plus the roller equals the full price of the paint. The correct equation to represent this situation is \((A)0.7p + 13.5 = p\), because \(0.7p\) represents the price of the paint after a \(30\%\) discount. Let's solve for \(p\), the full price of the paint.
  2. Isolate \(p\): To isolate \(p\) on one side of the equation, we subtract \(0.7p\) from both sides of the equation \(0.7p + 13.5 = p\). This gives us \(13.5 = p - 0.7p\).
  3. Combine Like Terms: Combining like terms on the right side of the equation, we get \(13.5 = 0.3p\).
  4. Divide to Find p: To find the value of \(p\), we divide both sides of the equation by \(0.3\).\(\newline\)So, \(p = \frac{13.5}{0.3}\).
  5. Calculate Final Price: Calculating the division, we get \(p = 45\).\(\newline\)Therefore, the full price of one gallon of paint is \(45\) \(\$\).

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