Problem 6 - 1,001 GED Practice Questions For Dummies

Question

Alex earns a weekly base salary of \(\$ 650\) as a car salesman. He also earns a \(9 \%\) commission on his monthly sales after the first \(\$ 10,000\). What was his total salary this month if he sold 7 cars whose average price was \(\$ 4,500\) each? (A) \(\$ 1,935\) (B) \(\$ 2,585\) (C) \(\$ 2,835\) (D) \(\$ 3,485\)

Step-by-Step Solution

Answer

Alex's total salary for the month is \(\$4535\).

Step 1: Calculate Monthly Base Salary

Since Alex earns a weekly base salary of \(\$650\), we will need to find his total base salary for the month. Since there are 4 weeks in a month, we can multiply his weekly salary by 4: \[ (\$650)(4) = \$2600 \] Alex's monthly base salary is \(\$2600\).

Step 2: Calculate Monthly Sales

Next, we need to calculate the total amount of sales Alex made this month. We know he sold 7 cars which had an average price of \(\$4500\) each. So, we can find the total sales by multiplying the number of cars by the average price: \[ (7)(\$4500) = \$31500 \] Alex's total sales for the month was \(\$31500\).

Step 3: Determine Commissionable Sales

Now, we need to calculate the sales amount on which Alex earned a \(9\%\) commission. We know that he earns this commission on sales after the first \(\$10000\). So, we can subtract \(\$10000\) from the total monthly sales: \[ \$31500 - \$10000 = \$21500 \] Alex earned a commission on \(\$21500\) worth of sales.

Step 4: Calculate Monthly Commission

Now, we can find the amount of commission Alex earned on the \(\$21500\) of sales. We can multiply this amount by \(9 \%\) to find his commission: \[ (\$21500)(0.09) = \$1935 \] Alex's commission for the month is \(\$1935\).

Step 5: Calculate the Total Salary

Finally, to find Alex's total salary for the month, we can simply add his base salary and the commission he earned: \[ \$2600 + \$1935 = \$ 4535 \] Alex's total salary for the month is \(\$4535\). Since none of the provided options match our result, it could signify a mistake in either the problem or the solution. However, we have followed the steps correctly, so the given options are likely incorrect.

Key Concepts

commission calculation

Calculating a commission involves understanding how much extra income is earned from a percentage of sales beyond a certain threshold. In Alex's case, the commission rate is 9% on sales exceeding $10,000. To find the commissionable amount, subtract the base amount (here, $10,000) from total sales (which is $31,500 in Alex's scenario).
This results in $21,500 of commissionable sales. We then calculate the commission by multiplying $21,500 by 9% (or 0.09 in decimal form).

• The calculation is: $21,500 × 0.09 = $1,935.
• This commission is added to the base salary to determine the total salary.

Understanding how to calculate commissions is crucial as it forms a significant part of the total income for many sales-based professions.

monthly salary calculation

Monthly salary calculation encompasses both a fixed base amount and any added earnings through commissions or bonuses. In Alex's example, his base salary is a weekly wage of $650.
To calculate his monthly earnings, multiply the weekly salary by four weeks in a month:

• Weekly Salary Formula: $650 × 4 = $2,600 monthly

This base serves as the guaranteed income regardless of performance. The additional earnings through commission depend on the amount sold beyond a base sales threshold. Combining these two components— base and commission—yields Alex's total salary for the month.
By systematically adding the commission ($1,935) to the monthly base salary ($2,600), Alex's total earnings amount to $4,535.
Knowing this process helps individuals better estimate their potential income and manage financial expectations.

math word problems

Math word problems help bridge practical situations with mathematical calculations. They often involve real-life scenarios like budgeting, shopping, or earning salary which can be confusing without structured problem-solving.
With Alex's salary problem, the scenario involves calculating sales commissions and base salaries. To tackle this, break down the problem into smaller, logical steps for clarity:

• Identify given data: Weekly salary, number of cars sold, and average price per car.
• Determine required figures: Total sales, commissionable sales, and overall earnings.

By organizing the problem into step-by-step calculations, solving becomes manageable and can be applied to similar word problems in everyday situations.

sales commission problems

Sales commission problems test your understanding of how sales contributes to income. These involve calculating commissions on sales exceeding a predetermined threshold and then integrating results with any fixed salary components.
In the problem with Alex, we start by calculating total car sales through multiplying the number of cars by their average price.

• Total Sales Calculation: 7 cars × $4,500 each = $31,500

Next, determine the sales amount eligible for commission, beyond the initial $10,000.
Finally, solve for the commission income and combine it with the base salary.

• Commission Amount: (Total Sales - Threshold) × Commission Rate
• Total Salary: Base Salary + Commission

Practicing such problems enhances one’s ability to efficiently calculate variable income components, vital for many careers in sales.