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Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis, each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with a maximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weekly salary is $900.

The weekly paycheck amount for each salesman, p, is a function of the number of sales, s, they had in that week.
Is the function representing the weekly paycheck amount of Salesman A a proportional relationship? Use complete sentences to explain your reasoning.
Is the function representing the weekly paycheck amount of Salesman B a proportional relationship? Use complete sentences to explain your reasoning.
Is the function representing the weekly paycheck amount of Salesman C a proportional relationship? Use complete sentences to explain your reasoning.

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Answer:

See below

Step-by-step explanation:

  • Proportional relationship formula:
  • y = kx

As per given we have:

Salesman A

  • p(s) = 65s  (p = $1300 maximum)
  • This is a proportional relationship,  $65 per each sale. But this is restricted to 20 sales.
  • Answer is yes (ignoring the restriction)

Salesman B

  • p(s) = 40s + 300
  • This is a linear but not proportional relationship
  • Answer is no

Salesman C

  • p(s) = 900
  • There is no relationship between sales number and weekly earning as it is a fixed salary
  • Answer is no

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Step-by-step explanation: