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.

Question

Which equation can you use to find p, the full price of one gallon of paint?
What is the full price of one gallon of paint?
$

Answer 1

Let's denote the full price of a gallon of paint as \( p \).

1. First Option: Buying a gallon of paint at a 30% discount and then paying for the roller:

   • The price she pays for the paint will be \( 0.7p \) (because she gets 30% off).
   • The total cost for this option will be \( 0.7p + 13.50 \).

2. Second Option: Paying full price for the paint and getting the roller for free:

   • The total cost in this case will simply be \( p \).

According to Meg, both options cost the same, so we can set up the equation: \[ 0.7p + 13.50 = p \]

Now, let's solve for \( p \): \[ 0.7p + 13.50 = p \] Subtract \( 0.7p \) from both sides: \[ 13.50 = p - 0.7p \] \[ 13.50 = 0.3p \] Now, divide both sides by \( 0.3 \): \[ p = \frac{13.50}{0.3} \] Calculating that gives: \[ p = 45 \]

Thus, the full price of one gallon of paint is $45.