Question

Al's commission for selling homes works out so he gets \(\$ 0.0125\) out of every dollar of the sales price. What is Al's commission on a \(\$ 150,000\) house? A. \(\$ 187.50\) B. \(\$ 1,687.50\) C. \(\$ 1,875.00\) D. \(\$ 18,750.00\)

Short answer

\(\$1,875\)

Step-by-step solution

Identify the commission rate

Determine Al's commission rate, which is given as \(\text{0.0125}\) or \(\text{1.25}\text{\text%}\)

Identify the sales price

The sales price of the house is \(\text{\text{\text{\text{\$150,000}}}}\)

Calculate the commission

Multiply the commission rate by the sales price to find Al's commission: \[ \text{\text{\text{\$150,000}}} \times 0.0125 = \text{\text{\text{\$1,875}}} \]

Key concepts

Percentage

Understanding percentages is vital to solving commission-based problems. A percentage represents a part of a whole and is expressed as a fraction of 100. For instance, if we say 1.25%, it means 1.25 parts out of every 100. In this exercise, Al’s commission rate is 1.25%, which means for every dollar he earns 1.25 cents.
To convert percentages into a decimal for calculations, you divide by 100. So, 1.25% becomes 0.0125. This step is crucial for accurately multiplying with the sales price to find the commission. Without mastering this, you'll find it challenging to proceed with the subsequent steps.

Multiplication

Multiplication is a fundamental mathematical operation used here to calculate the commission. Once you have the commission rate as a decimal (0.0125), you multiply it by the sales price of the item to find the amount of money earned.
In this case, if the sales price of a house is \(150,000, you multiply 0.0125 by 150,000. It’s helpful to break this down:

• First, multiply 150,000 by 0.01 (1%), which is 1,500.
• Then, multiply the remaining 0.0025 by 150,000, which is 375.

Finally, add the two results (1,500 + 375) to get \)1,875. Doing multiplication in steps like this can make the process clearer and easier to handle.

Sales Price

The sales price is the amount for which an item is sold. In a commission calculation, knowing the exact sales price is essential as it directly impacts the amount of commission earned.
For Al, the sales price is $150,000. This figure is given in the problem and is what we use to calculate his commission. Remember, in many real-world scenarios, sales prices can vary, so always ensure you have the correct figure before making any calculations.

Problem Solving

Effective problem-solving in math requires breaking down the problem into manageable steps. Here’s how it’s done for commission calculation:

• Identify the commission rate and understand it in both percentage and decimal form.
• Confirm the sales price of the item.
• Use multiplication to find the commission by multiplying the sales price by the decimal form of the commission rate.

Following these methodical steps ensures you arrive at the correct solution. If you run into issues, review each step to spot and correct any errors. This structured approach not only aids in solving this specific problem but also equips you with skills for tackling similar problems in the future.