A graduated commission employee makes $3.5\%$ interest on the first $\$50,000$ in sales and $6.5\%$ interest on all sales over $\$50,000$. Which of the following expressions represents the employee's total earnings on $\$81,500$ in sales?
a. $(0.035)(50,000)+(0.065)(81,500)$
b. $(0.035)(50,000)+(0.065)(31,500)$
c. $(0.35)(50,000)+(0.65)(31,500)$
d. $(3.5)(50,000)+(6.5)(31,500)$
Answer (2)
Calculate the sales exceeding $50,000: $81,500 - $50,000 = $31,500.
Calculate the commission on the first 50 , 000 : (0.035)($50,000). - Calculate the commission on the sales exceeding 50 , 000 : (0.065)($31,500).
Add the two commission amounts to find the total earnings: ( 0.035 ) ( 50 , 000 ) + ( 0.065 ) ( 31 , 500 ) .
Explanation
Understanding the Problem The problem states that the employee earns a commission of 3.5% on the first $50,000 in sales and 6.5% on any sales exceeding $50,000. The employee's total sales are $81,500. We need to determine which expression correctly calculates the employee's total earnings.
Calculating Sales Over $50,000 First, we need to calculate the amount of sales that exceed $50,000. This is done by subtracting $50,000 from the total sales of 81 , 500 : 81 , 500 − 50 , 000 = 31 , 500 $
So, the sales exceeding $50,000 are $31,500.
Commission on First $50,000 Next, we calculate the commission earned on the first $50,000 in sales. This is 3.5% of $50,000, which can be written as 0.035 * $50,000.
Commission on Sales Over $50,000 Then, we calculate the commission earned on the sales exceeding $50,000. This is 6.5% of $31,500, which can be written as 0.065 * $31,500.
Total Earnings Expression Finally, we add the two commission amounts to find the total earnings. The expression for the total earnings is: ( 0.035 ) ( 50 , 000 ) + ( 0.065 ) ( 31 , 500 ) Comparing this expression with the given options, we find that option B matches our calculated expression.
Final Answer Therefore, the correct expression representing the employee's total earnings on 81 , 500 in s a l es i s : ( 0.035 ) ( 50 , 000 ) + ( 0.065 ) ( 31 , 500 ) $
Examples
Imagine you're a real estate agent earning graduated commissions. You get 3% on the first $100,000 of a home sale and 5% on anything above that. If you sell a house for $350,000, this problem helps you calculate your total commission. You'd calculate 3% of $100,000 and 5% of the remaining $250,000, then add those amounts to find your total earnings. This type of calculation is fundamental in understanding how graduated commissions work in sales and finance.
The correct expression to calculate the employee's total earnings on 81 , 500 in s a l es i s (0.035)(50,000) + (0.065)(31,500)$. This correctly reflects earning 3.5% on the first $50,000 and 6.5% on the remaining $31,500 in sales. Thus, the chosen option is b .
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