eb is ordering two pizzas, and she is trying to figure out which of her coupons will give her the best deal. One coupon allows her to buy a pizza at full price and get a second pizza for half off. Another coupon gives her $12 off the total if she buys two pizzas at full price. After considering her options, Deb realizes that the total cost would be the same with either coupon.

Question

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

Answer 1

Let's denote the full price of one pizza as \( p \).

1. Using the first coupon (Buy one pizza at full price, get the second pizza at half off):

   • The cost of the first pizza is \( p \).
   • The cost of the second pizza at half off is \( \frac{p}{2} \).
   • Therefore, the total cost using this coupon is: \[ \text{Total Cost 1} = p + \frac{p}{2} = \frac{2p}{2} + \frac{p}{2} = \frac{3p}{2} \]

2. Using the second coupon (Get $12 off the total if she buys two pizzas at full price):

   • The cost of two pizzas at full price is \( 2p \).
   • After applying the $12 discount, the total cost using this coupon is: \[ \text{Total Cost 2} = 2p - 12 \]

Since Deb realizes that the total cost would be the same with either coupon, we can set the two total costs equal to each other: \[ \frac{3p}{2} = 2p - 12 \]

Now, we can solve this equation for \( p \):

1. First, eliminate the fraction by multiplying the entire equation by 2: \[ 3p = 4p - 24 \]

2. Now, isolate \( p \) by moving \( 4p \) to the left side: \[ 3p - 4p = -24 \] \[ -p = -24 \]

3. Finally, multiplying both sides by -1 gives: \[ p = 24 \]

Thus, the full price of one pizza is $24.