- The commission is calculated by multiplying the price by the commission rate, which is \(\$225 \times 0.15 = \$33.75\).
- The expression \((225)(0.15)\) is correct as it directly represents the commission.
- The expression \(225 - [(225)(0.85)]\) is also correct because it represents the total price minus the artist's share (\(85\%\) of the price), which leaves the shop's commission.
- The two correct expressions are \((225)(0.15)\) and \(225 - [(225)(0.85)]\).
- Final Answer: \(\boxed{(225)(0.15), 225 - [(225)(0.85)]}\)
Explanation
- Analyzing the commission calculation
The problem asks us to determine the commission earned by a shop on an artwork piece priced at \(\$225\), given a commission rate of \(15\%\). The commission is the amount the shop keeps from the sale, calculated as a percentage of the total price. We need to identify two equivalent expressions from the given choices that represent this amount. We know that a percentage can be written as a decimal: \(15\% = \frac{15}{100} = 0.15\). Thus, the commission can be calculated directly as the total price multiplied by the decimal form of the commission rate.
- Evaluating the first expression
The direct calculation for the commission is \(\text{Price} \times \text{Commission Rate}\). Substituting our values, we get \(\$225 \times 0.15\). This matches the first option: \((225)(0.15)\). Calculating this value gives \(\$225 \times 0.15 = \$33.75\). This is the exact amount the shop receives as commission.
- Evaluating the remaining expressions and identifying the correct ones
Now consider the expression \(225 - [(225)(0.85)]\). This expression represents the total price minus the amount the artist keeps. If the shop receives a \(15\%\) commission, then the artist receives \(100\% - 15\% = 85\%\) of the sale price. Therefore, the amount the artist keeps is \(225 \times 0.85\). Subtracting this from the total price leaves the amount the shop received as commission: \(\$225 - (\$225 \times 0.85) = \$225 - \$191.25 = \$33.75\). This matches the commission we calculated, so this expression is also correct. Checking the other options, \(225 - [(225)(0.15)]\) results in the amount the artist keeps, and \((225)(1.15)\) represents the price plus the commission, neither of which is the commission amount.
Examples
Calculating commissions correctly is a vital skill in business. For instance, if you were a real estate agent or a freelance artist selling your work through a gallery, understanding how to calculate your net earnings versus the gallery's cut helps you manage your finances. Knowing that a commission can be expressed as a simple percentage of the total or as the difference between the total price and the artist's share allows you to verify your earnings accurately. This mathematical foundation is used daily in retail, sales, and contract negotiations.