To expand the expression \(0.05(50 + 40)\) using the distributive property, you would distribute \(0.05\) to both terms inside the parentheses:
\[ 0.05(50) + 0.05(40) \]
Calculating those products:
\[ 0.05 \times 50 = 2.5 \] \[ 0.05 \times 40 = 2.0 \]
So, the expanded expression is:
\[ 2.5 + 2.0 \]
The total tax using the new expression is:
\[ 2.5 + 2.0 = 4.5 \]
This means that the total tax calculated using the original expression \(0.05(50 + 40)\) is also \(4.5\).
Expression That Calculates Total Cost First
The expression that involves finding the total cost first and then calculating the tax on that total would be:
\[ \text{Total Cost} = 50 + 40 \]
Once you find that total, you then calculate:
\[ \text{Tax} = 0.05 \times \text{Total Cost} = 0.05 \times (50 + 40) \]
This method gives the same total tax of \(4.5\).
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