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 salesa base salary of $20,000 per year with a commission of 5% of your saleshow 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 salesa base salary of $25,000 per year with a commission of 3% of your saleshow much you need to sell for option a to pay more?

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)

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.

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))