Question

Mrs. Robinson, an insurance agent, earns a salary of $4,800 per year plus a 3% commission on her sales. The average price of a policy she sells is $6,100.
Write an inequality to find how many policies Mrs. Robinson must sell to make an annual income of at least $8,000.

4800+183x<(line under the arrow)=8000
4800+183x=8000
4800+183x>=8000
4800+186>(ine under the arrow)=8000

Answer 1

Answer:

$4800+183x\geq 8000$

She must sell at least 18 policies to make an annual income of at least $8,000

Step-by-step explanation:

Let $x$ 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%:

$\frac{3*6,100}{100} =183$

Now we know that she makes $183 per policy sold. Since $x$ is the number of policies sold, $183x$ is her total commission for selling $x$ 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:

$4800+183x$

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:

$4800+183x\geq 8000$

Let's solve the inequality:

1. Subtract 4800 from both sides

$4800-4800+183x\geq 8000-4800$

$183x\geq 3200$

2. Divide both sides by 183

$\frac{183x}{183} \geq \frac{3200}{183}$

$x\geq 17.48$

Since she can't sell a fraction of a policy, we must round the result to the next integer:

$x\geq 18$

We can conclude that she must sell 18 policies to make an annual income of at least $8,000.