Answer:
[tex]4800+183x\geq 8000[/tex]
She must sell at least 18 policies to make an annual income of at least $8,000
Step-by-step explanation:
Let [tex]x[/tex] be the number of policies Mrs. Robinson must sell
We know that Mrs. Robins makes 3% on commission for each policy sold. We also know that the average price of a policy is $6,100, so she makes 3% of $6,100 per policy sold. To find the 3% of $6,100 we just need to multiply 3% and $6,100; then dive the result by 100%:
[tex]\frac{3*6,100}{100} =183[/tex]
Now we know that she makes $183 per policy sold. Since [tex]x[/tex] is the number of policies sold, [tex]183x[/tex] is her total commission for selling [tex]x[/tex] policies.
We also know that She makes $4,800 per year, so her total annual income is her salary plus her commissions, in other words:
[tex]4800+183x[/tex]
Finally, we know that she wants to make at least $8,000, so her salary plus her commissions must be greater or equal than $8,000:
[tex]4800+183x\geq 8000[/tex]
Let's solve the inequality:
1. Subtract 4800 from both sides
[tex]4800-4800+183x\geq 8000-4800[/tex]
[tex]183x\geq 3200[/tex]
2. Divide both sides by 183
[tex]\frac{183x}{183} \geq \frac{3200}{183}[/tex]
[tex]x\geq 17.48[/tex]
Since she can't sell a fraction of a policy, we must round the result to the next integer:
[tex]x\geq 18[/tex]
We can conclude that she must sell 18 policies to make an annual income of at least $8,000.
