Question

8. When hired at a new job a a salesperson you are given two pay options:

A base salary of $17,000 per year with a commission of 12% of your sales

A base salary of $20,000 per year with a commission of 5% of your sales

How much you need to sell for option A to pay more?

9. When hired at a new job as a salesperson you are given two pay options:

A base salary of $20,000 per year with a commission of 9% of your sales

A base salary of $25,000 per year with a commission of 3% of your sales

How much you need to sell for option A to pay more?

Answer 1

Solution 8:

We are given base salary of 17000 and 12% of sales.

Les us say salesperson does sales of x amount.

So 12% of x is 0.12x

Total salary = 17000+0.12x

In second case base salary is $20000 and commission of 5% of sales.

Total salay=20000+0.05x

Now for option A to pay more we have:

`17000+0.12x>20000+0.05x`

Solving we get:

`0.07x>3000`

x>42,857

Answer: Option A need to make sales of $42,857 more.

Solution 9:

We are given base salary of 20000 and 9% of sales.

Les us say salesperson does sales of x amount.

So 9% of x is 0.09x

Total salary = 20000+0.09x

In second case base salary is $25000 and commission of 3% of sales.

Total salay=25000+0.03x

Now for option A to pay more we have:

`20000+0.09x>25000+0.03x`

Solving we get:

`0.06x>5000`

x>83,333.33

Answer: Option A need to make sales of $83,333.33 more.

Answer 2

You can write equations for total pay, but in the end, you want to find the amount of sales that makes the difference in commission make up for the difference in base pay.

... (commission rate difference) × sales = (base pay difference)

To find the sales, divide by its coefficient:

... sales = (base pay difference)/(commission rate difference)

8.

Sales = (20,000 -17,000)/(.12 -0.05) = 3000/0.07 ≈ 42,857.14

You need to sell more than $42,857.14 for option A to pay more.

9.

Sales = (25,000 -20,000)/(.09 -.03) = 5000/0.06 ≈ 83,333.33

You need to sell more than $83,333.33 for option A to pay more.

_____

In each case, total pay is ...

... total pay = (base pay) + (commission rate) × sales

For the two options to give the same total pay, the difference in total pay is zero. That occurs when ...

... 0 = (base pay₁) + (commission rate₁) × sales -((base pay₂) + (commission rate₂) × sales)

... 0 = (base pay₁) - (base pay₂) - sales × ((commission rate₁) -(commission rate₂))

Solving for sales, we get the above result:

... sales = ((base pay₂) -(base pay₁))/((commission rate₁) -(commission rate₂))