Final answer:
To earn a total of $4,000 in one month, the employee must sell $56,000 worth of products. This is because they earn a 2% commission on sales beyond the first $6,000 and already receive a base salary of $3,000.
Step-by-step explanation:
The student's question is about calculating the sales needed to earn a total monthly income, including base salary and commission, in a given sales job.
To solve this problem, let's set up an equation based on the employee's earnings:
- The base salary is $3,000 per month.
- The commission is 2% (0.02) for all sales over $6,000.
- The target total earnings for the month is $4,000.
Let x represent the total amount of sales the employee needs to make in the month. The first $6,000 of sales does not earn a commission, so we will apply the commission only to sales beyond this amount:
Total earnings = Base salary + Commission on sales over $6,000
$4,000 = $3,000 + 0.02(x - $6,000)
To find , we rearrange the equation:
1. Subtract the base salary from both sides to isolate the commission: $4,000 - $3,000 = 0.02(x - $6,000)
2. This gives us $1,000 = 0.02(x - $6,000).
3. To solve for , divide both sides by 0.02: $6,000 = $1,000 / 0.02
4. This results in $6,000 = $50,000
5. Finally, add $6,000 to both sides to find the total sales: = $50,000 + $6,000 = $56,000.
Therefore, the employee must make $56,000 in sales to earn a total of $4,000 for the month.