on office equipment sales representative earns a weekly salary and commission on his sales. one week his total compensation on sales of $7000 was $700, the next week his total compensation on sales of $8000 was $740, find the weekly salary and commission rate
treat the data as two ordered pairs of the type
(s,c) where s is sales and c is commission.
so you have (7000,700) and (8000,740)
slope = (740-700)/(8000-7000)
= 40/1000 = .04
so c = .04s + b , (compare with y = mx+b )
for (7000,700)
700 = .04(7000) + b
b = 420
c = .04s + 420
his base salary is 420 and his rate of commission is 4%
To find the weekly salary and commission rate of the office equipment sales representative, we can set up a system of equations based on the given information.
Let's assume the weekly salary is denoted by S, and the commission rate as a decimal is denoted by R.
According to the first week's information:
Total compensation = Weekly salary + Commission
$700 = S + (R * $7000) ----(Equation 1)
Similarly, according to the second week's information:
Total compensation = Weekly salary + Commission
$740 = S + (R * $8000) ----(Equation 2)
We now have a system of two equations involving two variables. To solve this system, we can use the method of substitution or elimination.
Let's solve it using the method of substitution:
From Equation 1, we can express S in terms of R as:
S = $700 - (R * $7000)
Substituting this value of S into Equation 2 to eliminate S:
$740 = ($700 - (R * $7000)) + (R * $8000)
$740 = $700 - (R * $7000) + (R * $8000)
$740 = $700 + R * ($8000 - $7000)
$740 = $700 + R * ($1000)
$740 = $700 + $1000R
Now, we can solve this equation for R:
$740 - $700 = $1000R
$40 = $1000R
R = $40 / $1000
R = 0.04
The commission rate is 0.04 or 4% (as a decimal).
To find the weekly salary, substitute the value of R into Equation 1:
$700 = S + (0.04 * $7000)
$700 = S + $280 (by simplifying the expression)
$700 - $280 = S
S = $420
The weekly salary is $420.
Therefore, the weekly salary of the office equipment sales representative is $420 and the commission rate is 4%.