Question

a salesperson receives a base salary of $35,000 and a commission of 10% of the total sales for the year. write a linear model to help solve this question: if the salesperson sells $250,000 worth of merchandise, what is her total income for the year, including her base salary?

Explanation:

Step1: Define the linear model

Let \( I \) be the total income and \( S \) be the total sales. The base salary is $35,000 and the commission is 10% of sales, so the linear model is \( I = 35000 + 0.10S \).

Step2: Substitute the sales value

We know \( S = 250000 \). Substitute this into the model: \( I = 35000 + 0.10\times250000 \).

Step3: Calculate the commission

First, calculate \( 0.10\times250000 = 25000 \).

Step4: Calculate the total income

Then, add the base salary: \( I = 35000 + 25000 = 60000 \).

Answer:

The total income for the year is $60,000.