Anthony sells cars. Each month, he is paid $2,000, plus a $15 \% commission on monthly sales above $20,000. Which function calculates his monthly earnings $(E)$ as a function of $m$, his monthly sales?
$E(m)=2,000+0.15(m-20,000)$
$E(m)=2,000+0.15(m+20,000)$
$E(m)=2,000+15(m-20,000)$
$E(m)=2,000+15(m+20,000)$
Answer (1)
Anthony's base salary is $2,000.
He earns a 15% commission on sales above $20,000.
The commission is calculated as 0.15 ( m − 20 , 000 ) when 20,000"> m > 20 , 000 .
Therefore, the function for his earnings is E ( m ) = 2 , 000 + 0.15 ( m − 20 , 000 ) .
Explanation
Problem Analysis Let's analyze the problem. Anthony receives a base salary of $2,000 each month. Additionally, he earns a 15% commission on any sales exceeding $20,000. We need to determine the function E(m) that accurately calculates his total monthly earnings based on his monthly sales, m.
Earnings Calculation If Anthony's monthly sales, m, are less than or equal to $20,000, he only receives his base salary of $2,000. However, if his sales exceed $20,000, he earns a 15% commission on the amount exceeding $20,000, in addition to his base salary. This can be expressed mathematically as:
If 20,000"> m > 20 , 000 , then the commission is 0.15 × ( m − 20 , 000 ) .
Therefore, his total earnings, E(m), would be 2 , 000 + 0.15 × ( m − 20 , 000 ) .
Function Determination Based on the analysis, the function that calculates Anthony's monthly earnings (E) as a function of his monthly sales (m) is:
E ( m ) = 2 , 000 + 0.15 ( m − 20 , 000 )
Final Answer Comparing this with the given options, we find that the correct function is:
E ( m ) = 2 , 000 + 0.15 ( m − 20 , 000 )
Examples
Understanding commission-based earnings is crucial in many sales jobs. For instance, if a real estate agent earns a base salary plus a commission on sales above a certain threshold, this formula helps calculate their total income. Suppose an agent has a base salary of $3,000 and earns a 3% commission on sales above $100,000. If their sales for a month are $250,000, their total earnings would be calculated as 3 , 000 + 0.03 × ( 250 , 000 − 100 , 000 ) = $7 , 500 . This calculation helps them understand their potential earnings and plan accordingly.
