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% off, then pay 13.50 $ 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. Which equation can you use to find p, the full price of one gallon of paint? Choices: (A)0.3p + 13.5 = p (B)0.7p + 13.5 = p What is the full price of one gallon of paint? ____ $

Question

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% off, then pay 13.50 $ 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. Which equation can you use to find p, the full price of one gallon of paint?   Choices: (A)0.3p + 13.5 = p (B)0.7p + 13.5 = p  What is the full price of one gallon of paint?   ____ $

Bytelearn · Accepted Answer

Analyze choices: Meg is considering two options for buying paint and a roller. In the first option, she gets a 30% discount on the paint and pays $13.50 for the roller. In the second option, she pays the full price for the paint and gets the roller for free. Since the total cost is the same in both scenarios, we can set up an equation to find the full price of the paint, p.Set up equation: Let's analyze the choices given: (A) 0.3p + 13.5 = p (B) 0.7p + 13.5 = p Choice (A) suggests that 30% of the full price plus the cost of the roller equals the full price of the paint, which doesn't make sense because it doesn't account for the discount. Choice (B) suggests that 70% of the full price (which is the price after a 30% discount) plus the cost of the roller equals the full price of the paint. This makes sense because if the paint is discounted by 30%, Meg is paying 70% of the full price. Therefore, the correct equation to use is (B) 0.7p + 13.5 = p.Solve equation: Now, let's solve the equation 0.7p + 13.5 = p for p. First, we subtract 0.7p from both sides to isolate p on one side of the equation. 0.7p + 13.5 - 0.7p = p - 0.7p This simplifies to: 13.5 = 0.3pSubtract and isolate: Next, we divide both sides of the equation by 0.3 to solve for p. 13.5 / 0.3 = 0.3p / 0.3 This gives us: p = 45

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