To find an equivalent expression for the total cost of an item with price \( p \) after applying a 6% sales tax, we can start with the expression \( p + 0.06p \).
Step-by-step calculations:
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Combine the terms: \[ p + 0.06p = 1p + 0.06p = (1 + 0.06)p = 1.06p \]
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Now, let's plug in \( p = 10 \): \[ 10 + 0.06(10) = 10 + 0.6 = 10.6 \] Now, if we calculate it with the equivalent expression \( 1.06p \): \[ 1.06(10) = 10.6 \]
Conclusion:
- The equivalent expression for the total cost including tax is \( 1.06p \).
- When using \( p = 10 \):
- From \( p + 0.06p \): \( 10.6 \)
- From \( 1.06p \): \( 10.6 \)
Both expressions yield the same result when \( p = 10 \).
So, the expressions are equivalent.