Question

A salesperson at an electronics store is given a choice of two different compensation plans. Plan A pays him a weekly salary of $250 plus a commission of $25 for each stereo sold. Plan B offers no salary but pays $50 commission on each stereo sold. How many stereos must the salesperson sell to make the same amount of money with both plans? Write a paragraph answering the following questions: When is plan B the better plan? When is plan A the better plan? Which plan would you select and why?

Answer 1

X= = number of stereos sold; a = amount of money earned 250 + 25x = a x = 10 stereos
50x = a a = $500

Answer 2

• A sales person must sell 10 stereos to earn the same salary with each plan.
• A sales person must sell more than 10 stereos to Plan B be better.
• A sales person must sell less than 10 stereos to Plan A be better.

Explanation:

According to the problem.

Plan A:

$250 per week.

$25 per stereo sold.

It's expressed as:
`250+25x`

Plan B:

No salary.

$50 per stereo sold.

It's expressed as:
`50x`

Now, to make the same amount of money with both plans we must solve the following equality

`50x=250+25x`

Then, we solve for
`x`

`-250=25x-50x\\-250=-25x\\x=(-250)/(-25)\\ x=10`

So, a sales person must sell 10 stereos to earn the same salary with each plan.

On the other hand, if plan B is better than plan A, it means the following inequality is true

`B>A\\50x>250+25x\\50x-25x>250\\25x>250\\x>(250)/(25) \\x>10`

Therefore, if a salesperson sells more than 10 stereos, then the Plan B is better.

If plan A is better, then the following relation is true.

`A>B\\250+25x>50x\\25x-50x>-250\\-25x>-250\\x<10`

Therefore, if a sales person sells less than 10 stereos, then Plan A is better than Plan B.