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 $5000 was $1000. The next week his total compensation on sales of $7000 was $1160.
Find Mr. Alexander's weekly salary and his commission rate.
A) weekly salary: $610
B) weekly salary: $600 commission rate: 7% commission rate: 8%
C) weekly salary: $590
D) weekly salary: $800 commission rate: 9% commission rate: 6%

Question

Quizplus · Accepted Answer

Let's define the weekly salary as x and the commission rate as y.

From the problem, we have the following two equations:

x + 0.2y = 1000    (equation 1)

x + 0.16y = 1160   (equation 2)

Where 0.2y represents the commission earned on sales of $5000, and 0.16y represents the commission earned on sales of $7000.

Now we can solve for x and y.

Subtracting equation 2 from equation 1:

0.04y = -160

y = -4000

This value of y is negative, which means it is not a valid commission rate. This happens because we made a mistake somewhere in our calculations. Let's check our work.

Starting with equation 1:

x + 0.2y = 1000

Substituting y = -4000:

x + 0.2(-4000) = 1000

x - 800 = 1000

x = 1800

So, our solution is:

x = 1800, y = -4000

This gives us a weekly salary of $1800, but a negative commission rate of -80%. This does not make sense, so we need to check our work again.

Let's try subtracting equation 1 from equation 2 this time:

0.04y = 160

y = 4000

Substituting y = 4000 into equation 1:

x + 0.2(4000) = 1000

x + 800 = 1000

x = 200

So, our new solution is:

x = 200, y = 4000

This gives us a weekly salary of $200, and a commission rate of 20%, which is a valid answer.

Therefore, our final answer is:

Answer: B

Mr. Alexander's weekly salary is $200, and his commission rate is 20%. Let's denote Mr. Alexander's weekly salary as $S$ and his commission rate as $C$.

From the problem, we can set up two equations:

$5000C + S = 1000$

$7000C + S = 1160$

Subtracting the first equation from the second equation, we get:

$2000C = 160$

$C = 0.08$

Substituting $C=0.08$ into either equation, we can solve for $S$:

$5000(0.08) + S = 1000$

$S = 610$

Therefore, Mr. Alexander's weekly salary is $610 and his commission rate is 8%. Choice B is the correct answer.

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