To solve this problem, we need to set up an equation based on the two coupon options that Deb has. Let's denote the full price of one pizza as \( p \).
Option 1: Buy one pizza at full price, get the second pizza for half off.
- The cost for the first pizza is \( p \).
- The cost for the second pizza at half price is \( \frac{p}{2} \).
- Therefore, the total cost for this option is: \[ \text{Total Cost Option 1} = p + \frac{p}{2} = \frac{2p}{2} + \frac{p}{2} = \frac{3p}{2} \]
Option 2: Buy two pizzas at full price with $12 off.
- The cost for two pizzas at full price is \( 2p \).
- After applying the $12 discount, the total cost is: \[ \text{Total Cost Option 2} = 2p - 12 \]
Since Deb realizes that the total cost would be the same with either coupon, we set the two total costs equal to each other:
\[ \frac{3p}{2} = 2p - 12 \]
Now, we can solve for \( p \):
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Multiply both sides by 2 to eliminate the fraction: \[ 3p = 4p - 24 \]
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Now, move \( 4p \) to the left side: \[ 3p - 4p = -24 \] \[ -p = -24 \]
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Multiply both sides by -1: \[ p = 24 \]
Thus, the full price of one pizza is: \[ \boxed{24} \]