Samantha Jones has a job offer in which she will receive #600 per month plus a commission of 2% of the total price of the cars she sells. At her current job, she receives $1000 per month plus a commission of 1.5% of her total sales.
a. What is the total price of the cars that Ms. Jones must sell each month to make the same income from either dealership? Explain.
b. How much must Ms. Jones sell to make the new job a better deal? Show all work.
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current pay: 1000 + .015s
new job pays: 600 + 0.2s
what value of s makes them equal?
600 + .2s = 1000 + .015s
.005s = 400
s = 80,000
any sales past that makes the new job a better deal, since she gets more per sale.
005s = 400
s = 80,000
To find the answers to these questions, we need to set up equations and solve for the unknown variables. Let's break it down step by step:
a. To determine the total price of the cars that Ms. Jones must sell each month to make the same income from either dealership, we can equate her monthly income at the current job to her monthly income at the new job.
For the current job:
Income = $1000 + 1.5% of total sales
For the new job:
Income = $600 + 2% of total price of the cars sold
Now we can set these two expressions equal to each other and solve for the total price of the cars sold.
$1000 + 0.015(total sales) = $600 + 0.02(total price of cars sold)
We are given that the total sales are equal to the total price of the cars sold. So we can simplify the equation as follows:
$1000 + 0.015(total price of cars sold) = $600 + 0.02(total price of cars sold)
Now we can solve for the total price of the cars sold.
0.015(total price of cars sold) - 0.02(total price of cars sold) = $600 - $1000
-0.005(total price of cars sold) = -$400
Dividing both sides of the equation by -0.005, we get:
total price of cars sold = -$400 / -0.005
total price of cars sold = $80,000
Therefore, to make the same income from either dealership, Ms. Jones must sell cars with a total price of $80,000 each month.
b. To determine how much Ms. Jones must sell to make the new job a better deal, we need to compare her income at the current job to her income at the new job, given the total sales or total price of cars sold.
For the current job:
Income = $1000 + 1.5% of total sales
For the new job:
Income = $600 + 2% of total price of the cars sold
We want to find the threshold where the income at the new job exceeds the income at the current job, thus making it a better deal for Ms. Jones.
$600 + 0.02(total price of cars sold) > $1000 + 0.015(total sales)
Simplifying this inequality, we get:
0.02(total price of cars sold) - 0.015(total sales) > $1000 - $600
0.02(total price of cars sold) - 0.015(total sales) > $400
Now, substitute the total sales with the total price of cars sold:
0.02(total price of cars sold) - 0.015(total price of cars sold) > $400
0.005(total price of cars sold) > $400
Dividing both sides of the inequality by 0.005, we get:
total price of cars sold > $400 / 0.005
total price of cars sold > $80,000
So, Ms. Jones must sell cars with a total price greater than $80,000 to make the new job a better deal.
In summary, to make the same income from either dealership, Ms. Jones must sell cars with a total price of $80,000 each month. To make the new job a better deal, she must sell cars with a total price greater than $80,000.