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?

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vielmrlorgozz vielmrlorgozz · Answer 1 · 2018-11-04T01:55:34+01:00

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

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jajumonac jajumonac · Answer 2 · 2020-04-24T04:41:47+02:00

Answer:

Step-by-step explanation:

According to the problem.

$250 per week.

$25 per stereo sold.

It's expressed as: [tex]250+25x[/tex]

No salary.

$50 per stereo sold.

It's expressed as: [tex]50x[/tex]

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

[tex]50x=250+25x[/tex]

Then, we solve for [tex]x[/tex]

[tex]-250=25x-50x\\-250=-25x\\x=\frac{-250}{-25}\\ x=10[/tex]

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

[tex]B>A\\50x>250+25x\\50x-25x>250\\25x>250\\x>\frac{250}{25} \\x>10[/tex]

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.

[tex]A>B\\250+25x>50x\\25x-50x>-250\\-25x>-250\\x<10[/tex]

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