- The formula for calculating total monthly earnings is \(E = B + (R \times S)\).
- We calculated the earnings for each plan using Maya's monthly sales of \(\$5,000\).
- Comparing the results (\(\$900\), \(\$950\), \(\$1,000\), and \(\$1,050\)), we identify that Plan D provides the highest earnings.
- The highest monthly earnings are \(\boxed{\text{Plan D}}\).
Explanation
- Problem Analysis and Formula Setup
Maya's monthly earnings are determined by her base salary plus a commission calculated from her monthly sales. The formula for the total monthly earnings, \(E\), is:
\[E = B + (R \times S)\]
where:
- \(B\) is the monthly base salary,
- \(R\) is the commission rate, and
- \(S\) is the monthly sales, which is given as \(\$5,000\).
We need to calculate \(E\) for each of the four plans (A, B, C, and D) and compare them to find the one that yields the highest income.
- Calculating Earnings for Each Plan
Using the given sales amount of \(S = \$5,000\), we calculate the total monthly earnings for each plan:
- Plan A: \(E_A = \$500 + (0.08 \times \$5,000) = \$500 + \$400 = \$900\)
- Plan B: \(E_B = \$600 + (0.07 \times \$5,000) = \$600 + \$350 = \$950\)
- Plan C: \(E_C = \$700 + (0.06 \times \$5,000) = \$700 + \$300 = \$1,000\)
- Plan D: \(E_D = \$800 + (0.05 \times \$5,000) = \$800 + \$250 = \$1,050\)
- Comparison and Conclusion
Comparing the total monthly earnings calculated for each plan:
- Plan A: \(\$900\)
- Plan B: \(\$950\)
- Plan C: \(\$1,000\)
- Plan D: \(\$1,050\)
We observe that \(E_D > E_C > E_B > E_A\). Therefore, Plan D yields the highest monthly earnings for Maya with a total of \(\$1,050\). The correct choice is Plan D.
Examples
In real-life professional settings, commission-based jobs often present multiple pay structures to employees. By understanding how to calculate earnings using basic algebra, one can compare different offers to maximize their income. For example, if you are a salesperson, you might encounter plans with high base salaries but lower commission rates, or low base salaries with high commission potential. Calculating the total earnings based on your projected sales helps you select the structure that best aligns with your financial goals.