Let's break down the problem. We need to find out the total earnings of an employee from [tex]$81,500 in sales, given that:
- The employee earns $[/tex]3.5 \%[tex]$ (or 0.035 as a decimal) interest on the first $[/tex]50,000 in sales.
- The employee earns [tex]$6.5 \%$[/tex] (or 0.065 as a decimal) interest on all sales over [tex]$50,000.
Now, let's evaluate the provided options step by step:
1. First $[/tex]50,000 of sales:
[tex]\[
\text{Earnings} = 0.035 \times 50,000 = 1,750
\][/tex]
2. Sales above [tex]$50,000:
Total sales are $[/tex]81,500, so the amount above $50,000 is:
[tex]\[
81,500 - 50,000 = 31,500
\][/tex]
For this amount, the earnings will be:
[tex]\[
\text{Earnings} = 0.065 \times 31,500 = 2,047.5
\][/tex]
3. Total earnings:
Combining both the parts,
[tex]\[
\text{Total Earnings} = 1,750 + 2,047.5 = 3,797.5
\][/tex]
Now, let's evaluate each of the expressions:
- Option a. [tex]\((0.035)(50,000)+(0.065)(81,500)\)[/tex]:
[tex]\[
(0.035)(50,000) + (0.065)(81,500) = 1,750 + 5,297.5 = 7,047.5
\][/tex]
- Option b. [tex]\((0.035)(50,000)+(0.065)(31,500)\)[/tex]:
[tex]\[
(0.035)(50,000) + (0.065)(31,500) = 1,750 + 2,047.5 = 3,797.5
\][/tex]
- Option c. [tex]\((0.35)(50,000)+(0.65)(31,500)\)[/tex]:
[tex]\[
(0.35)(50,000) + (0.65)(31,500) = 17,500 + 20,475 = 37,975
\][/tex]
- Option d. [tex]\((3.5)(50,000)+(6.5)(31,500)\)[/tex]:
[tex]\[
(3.5)(50,000) + (6.5)(31,500) = 175,000 + 204,750 = 379,750
\][/tex]
Comparing all the calculated values with the accurate step-by-step breakdown, the correct answer is:
[tex]\[
\text{Option B}: (0.035)(50,000)+(0.065)(31,500)
\][/tex]
So, the best answer is:
B
