The table below shows the earnings, in thousands of dollars, for three different commissioned employees. $2,000 + 3% on all sale
s 7% on all sales 5% on the first $40,000 + 8% on anything over $40,000 December 4.4 5.6 5.2 January 3.5 3.85 3.6 February 4.7 4.9 4.4 Who had the largest dollar amount in sales for the month of January? a. The salary plus commission employee.
b. The straight commission employee.
c. The graduated commission employee. d. They each had the same dollar amount in sales.
The salary plus commission employee earned $3,500 in January. Let his amount of sales for the month of January be x, then $2,000 + 3% of x = $3,500.
0.03x = $3,500 - $2,000 = $1,500
x = $1,500 / 0.03 = $50,000
The straight commission employee earned $3,850 in January. Let his amount of sales for the month of January be y, then 7% of y = $3,850.
0.07y = $3,850
y = $3,850 / 0.07 = $55,000
The graduated commission employee earned $3,600 in January. Let his amount of sales for the month of January be z, then 5% of $40,000 + 8% of z = $3,600.
0.05 x 40,000 + 0.08z = $3,600
$2,000 + 0.08z = $3,600
0.08z = $3,600 - $2,000 = $1,600
z = $1,600 / 0.08 = $20,000
Total sales for the graduated commission employee<span> = $40,000 + $20,000 = $60,000
Therefore, the graduated commission employee had the largest dollar amount in sales of $60,000 for the month of January</span>
A line is perpendiculat to another which has a slope of m if the perpendicular line has a slope of -1/m. That means that if the product of slopes of two lines is -1, the two lines are perpendicular.
Here, y1=-7/4x, or m=-7/4 The perpendicular should have a slope of -1/m=-1/(-7/4)=4/7
