Question 419224: Don, an office equipment sales representative, earns a weekly salary plus a commission on his sales. On week his total comensation( weekly salary +commission amount) on sales of $4000was $660. The next week his total compensation on sales of $6000 was $740. Find Don's weekly salary and his commission rate.
Answer by duckness73(47)   (Show Source):
You can put this solution on YOUR website! Let s = Don's salary
Let p = Don's commission rate
Note that the dollar amount of Don's commission is a percent of the sales, so Don's dollar commission on sales of $4000 is 4000p and Don's dollar commission on sales of $6000 is 6000p. His salary is fixed, no matter how much he sells. So, using his compensation totals for the two weeks, we have:
In week 1: s + 4000p = 600
In week 2: s + 6000p = 740
Solving these two simultaneous equations, we have equation 1:
s = 600 - 4000p
Substituting into equations 2, we have
600 - 4000p + 6000p = 740
600 + 2000p = 740 (combining like terms)
2000p = 140 (subtracting 600 from both sides)
p = 0.07 (dividing both sides by 2000)
This means that Don's commission is 0.07 of sales, or 7%.
In figuring up Don's weekly salary, we can use either of the two equations, say equation 1:
s + 4000p = 600 (equation 1)
s + 4000(0.07) = 600 (substituting value for variable p)
s + 280 = 600 (simplifying the term)
s = 320 (subtracting 280 from both sides)
This Don's weekly salary is $320 and his commission rate is 7%
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