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Answer:
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%:
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:
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:
Let's solve the inequality:
1. Subtract 4800 from both sides
2. Divide both sides by 183
Since she can't sell a fraction of a policy, we must round the result to the next integer:
We can conclude that she must sell 18 policies to make an annual income of at least $8,000.