Answer:
![4800+183x\geq 8000](https://tex.z-dn.net/?f=4800%2B183x%5Cgeq%208000)
She must sell at least 18 policies to make an annual income of at least $8,000
Step-by-step explanation:
Let
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](https://tex.z-dn.net/?f=%5Cfrac%7B3%2A6%2C100%7D%7B100%7D%20%3D183)
Now we know that she makes $183 per policy sold. Since
is the number of policies sold,
is her total commission for selling
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](https://tex.z-dn.net/?f=4800%2B183x)
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](https://tex.z-dn.net/?f=4800%2B183x%5Cgeq%208000)
Let's solve the inequality:
1. Subtract 4800 from both sides
![4800-4800+183x\geq 8000-4800](https://tex.z-dn.net/?f=4800-4800%2B183x%5Cgeq%208000-4800)
![183x\geq 3200](https://tex.z-dn.net/?f=183x%5Cgeq%203200)
2. Divide both sides by 183
![\frac{183x}{183} \geq \frac{3200}{183}](https://tex.z-dn.net/?f=%5Cfrac%7B183x%7D%7B183%7D%20%5Cgeq%20%5Cfrac%7B3200%7D%7B183%7D)
![x\geq 17.48](https://tex.z-dn.net/?f=x%5Cgeq%2017.48)
Since she can't sell a fraction of a policy, we must round the result to the next integer:
![x\geq 18](https://tex.z-dn.net/?f=x%5Cgeq%2018)
We can conclude that she must sell 18 policies to make an annual income of at least $8,000.