To find the price after a 20% discount on the tagged price \( p \), you can follow these steps:
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Calculate the amount of the discount, which is 20% of \( p \). This can be expressed as: \[ \text{Discount} = 0.20 \times p \]
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Subtract the discount from the original price \( p \) to get the price after the discount: \[ \text{Price after discount} = p - (0.20 \times p) \]
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Factor out \( p \) from the expression: \[ \text{Price after discount} = p(1 - 0.20) \] \[ = p(0.80) \]
Thus, the expression that represents the price after the discount but before tax is: \[ 0.80p \]