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?
Which equation can you use to find p, the full price of one gallon of paint?
Answers
GPT-4o mini
To find the full price of one gallon of paint (denoted as \( p \)), we need to set up an equation based on the two options Meg has for purchasing paint and a roller.
**Option 1:** Buy a gallon of paint at a 30% discount and pay $13.50 for the roller.
The discounted price for the gallon of paint would be:
\[
p - 0.30p = 0.70p
\]
So, the total cost for this option would be:
\[
0.70p + 13.50
\]
**Option 2:** Buy a gallon of paint at full price and get the roller for free.
The total cost for this option is simply:
\[
p
\]
According to the problem, both options cost the same amount, so we can set the two expressions equal to each other:
\[
0.70p + 13.50 = p
\]
This is the equation you can use to solve for \( p \), the full price of one gallon of paint.
**Option 1:** Buy a gallon of paint at a 30% discount and pay $13.50 for the roller.
The discounted price for the gallon of paint would be:
\[
p - 0.30p = 0.70p
\]
So, the total cost for this option would be:
\[
0.70p + 13.50
\]
**Option 2:** Buy a gallon of paint at full price and get the roller for free.
The total cost for this option is simply:
\[
p
\]
According to the problem, both options cost the same amount, so we can set the two expressions equal to each other:
\[
0.70p + 13.50 = p
\]
This is the equation you can use to solve for \( p \), the full price of one gallon of paint.