Precalculus word problem

Question

Curt can be paid in one of two ways for the furniture he sells. Plan A: Salary of $750 per month, plus a commission of 10% sales. Plan B: Salary of $1050 per month, plus a commission of 15% of sales in excess of $7000. for what amount of monthly sales is plan B better than plan A, assuming Curt’s sales are always more than $7000?

Answer 1

Well, we will need an equation to solve this. Coming up with an equation for the first scenario is pretty easy:

(One quick note on commission, in case we don't know. Commission is a bonus paid out on a given per cent of a sale or total sales. )

750 + 0.10 (total sales)

We use 0.10 because it is ten per cent. Let's set total sales = x just to make writing easier.

750 + 0.10 x = total salary in the first scenario

The second scenario is a bit more difficult because Curt will only be paid commission on sales more than 7000. So really what we are doing is subtracting 7000 from his total sales and paying commission on whatever is left so for the second scenario the equation is:

1050 + 0.15 (x - 7000) = total salary in the second scenario

So now we do not set these two values equal but greater than as in:

750 + 0.10 x < 1050 + 0.15 (x - 7000)

multiply through the parentheses

750+0.10 x < 1050 + 0.15x - 1050

1050 - 1050 = 0

so we have: 750 + 0.10 x < 0.15x

subtract 0.10 x from both sides

750 < 0.05 x

Divide both sides by .05

15,000 < x

So Plan B is a better scenario than Plan A for all X > 15,000

Let's check this with 15001!

In scenario A, 750 +1500.1 = 2250.1

In scenario B, 1050 + (150001-7000).15 = 1050 + 1200.15 = 2250.15

It works!