Ms. Jones has two job offers as a car salesperson. At one dealership, she will receive $600 per month plus a commission of 2% of the total price of the automobiles she sells. At the other dealership, she will receive $1000 per month plus a commission of 1.5% of her total sales.
What is the total price of automobiles that Ms. Jones must sell each month to make the same income from either dealership?
I need help
To find the total price of automobiles that Ms. Jones must sell each month to make the same income from either dealership, we need to set up an equation and solve it.
Let's assume the total price of automobiles that Ms. Jones sells per month is x.
At the first dealership, her income will be the sum of her fixed monthly salary ($600) and the commission she earns on the total price of automobiles she sells (which is 2% of x).
So, her income at the first dealership is 600 + 0.02x.
At the second dealership, her income will be the sum of her fixed monthly salary ($1000) and the commission she earns on her total sales (which is 1.5% of x).
So, her income at the second dealership is 1000 + 0.015x.
To find the total price of automobiles she must sell to make the same income from either dealership, we set up the following equation:
600 + 0.02x = 1000 + 0.015x
Now, we can solve this equation to find the value of x:
0.02x - 0.015x = 1000 - 600
0.005x = 400
x = 400 / 0.005
x = 80,000
Therefore, Ms. Jones must sell automobiles with a total price of $80,000 each month to make the same income from either dealership.