To solve this problem, we need to set up an equation based on the information given about the two coupons.
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First coupon: Buy one pizza at full price and get a second pizza at half off.
- The cost for the first pizza: \( p \) (where \( p \) is the full price of one pizza).
- The cost for the second pizza at half off: \( \frac{p}{2} \).
- Total cost with the first coupon: \[ p + \frac{p}{2} = \frac{2p}{2} + \frac{p}{2} = \frac{3p}{2} \]
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Second coupon: Get $12 off the total if she buys two pizzas at full price.
- The cost for two pizzas at full price: \( 2p \).
- Total cost with the second coupon: \[ 2p - 12 \]
Now, since Deb realized that the total cost would be the same with either coupon, we can set up the following equation: \[ \frac{3p}{2} = 2p - 12 \]
To solve for \( p \), we'll first eliminate the fraction by multiplying the entire equation by 2: \[ 3p = 4p - 24 \]
Next, we will isolate \( p \) by rearranging the equation: \[ 3p - 4p = -24 \ -p = -24 \]
Multiplying both sides by -1 gives: \[ p = 24 \]
Thus, the full price of one pizza is $24.