A salesperson receives a base salary of $35,000 and a commission of 10% of the total sales for the year. a.) Write a linear model that shows the salesperson’s total income based on total sales of k dollars. b.) If the salesperson sells $250,000 worth of merchandise, what is her total income for the year, including her base salary?

Answer:

Part a) The linear model that shows the salesperson’s total income is equal to

Part b) The total income is

Step-by-step explanation:

Part a)

Let

k-------> the total sales for the year

y-----> the total income for the year

we know that

The linear equation that represent the situation is

Part b) we have

substitute the value of k in the linear model to find the total income

Final answer:

The salesperson's income is represented by the linear model y = 35000 + 0.10k. If they sell $250,000 of merchandise, their total income, including salary and commission, would be $60,000.

Explanation:

A) The total income of the salesperson can be represented by the linear equation y = 35000 + 0.10k, where y represents the total income including the base salary and commission, and k represents the total sales.

B) To calculate the total income for a certain amount of sales, you would substitute the total sales amount into the equation. If the salesperson sold $250,000 worth of merchandise, the total income would be y = 35000 + 0.10*250000 = 35000 + 25000 = $60,000.

The salesperson would earn a total of $60,000 including base salary and commission for the year for the sales of $250,000 worth of merchandise.

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