Question

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.

Answer 1

Answer:

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Step-by-step explanation:

For this, we let x be the number of items that each salesman sold and y be the total salary (summing up the base, commission, etc).

            Salesman A: y 65x + 1300

             Salesman B: y = 40x + 300 + C

             Salesman C: y = 900

Answer 2

Answer:

Let x represent the number of sales each man had.

For Salesman A, he earns $65 per sale; this is 65x.

For Salesman B, he earns $40 per sale; this is 40x.  We also add to this his weekly salary of $300; this gives us 40x+300.

Since their pay was equal, set the two expressions equal:

65x = 40x+300

Subtract 40x from each side:

65x-40x = 40x+300-40x

25x = 300

Divide both sides by 25:

25x/25 = 300/25

x = 12