Don, an office equipment sales representative, earns a weekly salary plus a commission on his sales. One week his total compensation on sales of $6000 was $600. The next week his total compensation on sales of $9000 was $690. Find don’s weekly salary and his commission rate

Question

Don, an office equipment sales representative, earns a weekly salary plus a commission on his sales. One week his total compensation on sales of $6000 was $600. The next week his total compensation on sales of $9000 was $690. Find don’s weekly salary and his commission rate

Answer 1

You have 2 equations you could be working with.

Firstly the form of the equations is
Earnings = Salary + (commission rate)x(sales)
In the first instance Don made
600 on 6000 in sales so
1) 600 = Salary + 6000x
on 9000 in sales he made $690
2) 690 = Salary + 9000x
If we re-arrange both for Salary we obtain
1) 600- 6000x = Salary
2) 690 - 9000x = Salary
By the "comparision method" since the right hand sides are equal we can set the left hand sides equal ... and solve for x
600- 6000x = 690 - 9000x
bring the x's to one side and the numbers to the other
- 6000x + 9000x = 690 - 600
3000x = 90
x = .03
So the commission rate is 3%
Now just sub that back into either equation 1) or 2) and solve for the salary : )

Answer 2

To find Don's weekly salary and his commission rate, we can set up a system of equations based on the given information.

Let's first define the variables:
S = Weekly salary
C = Commission rate

From the information provided, we have the following two equations:

1) S + C(6000) = 600
2) S + C(9000) = 690

Now, we can solve this system of equations. Let's start by isolating S in Equation 1:

S = 600 - C(6000)

Substitute this expression for S into Equation 2:

600 - C(6000) + C(9000) = 690

Simplify and combine like terms:

600 - 6000C + 9000C = 690

Combine the coefficients of C:

3000C = 90

Divide both sides by 3000:

C = 90 / 3000

C = 0.03

Now substitute the value of C back into Equation 1 to solve for S:

S = 600 - 0.03(6000)

S = 600 - 180

S = 420

Therefore, Don's weekly salary is $420 and his commission rate is 0.03 (or 3%).

Answer 3

To find Don's weekly salary and his commission rate, we need to set up a system of equations based on the given information.

Let's use the following variables:
- x: Don's weekly salary (in dollars)
- y: Don's commission rate (as a decimal)

Based on the first week's information, we can write the equation:
x + 0.01y * 6000 = 600

And based on the second week's information, we can write the equation:
x + 0.01y * 9000 = 690

Now, we have a system of two equations:
x + 0.01y * 6000 = 600
x + 0.01y * 9000 = 690

We can solve this system of equations using substitution or elimination method.

Let's solve it using substitution method:

1. Solve the first equation for x in terms of y:
x = 600 - 0.01y * 6000

2. Substitute x in the second equation with the expression found in step 1:
600 - 0.01y * 6000 + 0.01y * 9000 = 690

Now, solve this equation for y.

600 - 0.01y * 6000 + 0.01y * 9000 = 690
600 + 0.01y * 3000 = 690
0.01y * 3000 = 90
0.01y = 30
y = 30 / 0.01
y = 3000

Now that we have the value of y, we can substitute it back into one of the original equations to find x.

Using the first equation:
x + 0.01 * 3000 * 6000 = 600
x + 1800 = 600
x = 600 - 1800
x = -1200

Therefore, Don's weekly salary is -$1200 and his commission rate is 30% (expressed as a decimal). However, please note that the negative salary does not make sense in this context. Hence, there might be an error in the given information or calculations.