Solve the problem.
-Mr. Alexander earns a weekly salary plus a commission from his position as a salesman. One week his total compensation on sales of $4000 was $640. The next week his total compensation on sales of $3000 was $600.
Find Mr. Alexander's weekly salary and his commission rate.
A)weekly salary: $400
B)weekly salary: $490 commission rate: 4.8% commission rate: 3%
C)weekly salary: $470
D)weekly salary: $480 commission rate: 5% commission rate: 4%

Question

Quizplus · Accepted Answer

Let's start by setting up a system of equations:

S + 0.05(4000) = 640   (where S is the weekly salary and 0.05 is the commission rate as a decimal)
S + 0.04(3000) = 600   (where 0.04 is the commission rate as a decimal)

Simplifying these equations, we get:

S = 440
S = 480

Since we're looking for the weekly salary and commission rate, we can use either equation to find the commission rate. Using the first equation:

440 + 0.05(4000) = 640
440 + 200 = 640
200 = 200

So the commission rate is 5% and the weekly salary is $480.

Therefore, the answer is D. Let's first find the commission rate.

In the first week, Mr. Alexander earned a total of $640 on sales of $4000. This means that his commission rate was:

commission rate = (total compensation - weekly salary) / sales
commission rate = ($640 - weekly salary) / $4000

We can rearrange this formula to solve for the weekly salary:

weekly salary = $640 - commission rate x $4000

Similarly, in the second week, Mr. Alexander earned a total of $600 on sales of $3000. This means that his commission rate was:

commission rate = ($600 - weekly salary) / $3000

We can substitute the expression we found for weekly salary in the first formula into this second formula to get:

commission rate = ($600 - ($640 - commission rate x $4000)) / $3000
simplifying, we get:
commission rate = 0.04 or 4%

Now that we know the commission rate, we can use either of the original formulas to solve for the weekly salary:

weekly salary = $640 - 0.04 x $4000
weekly salary = $480

So the answer is D: weekly salary $480, commission rate 5%.

Solve the Problem. -Mr. Alexander Earns a Weekly Salary Plus a Commission from a Commission