Question

The table below shows the earnings, in thousands of dollars, for three different commissioned employees.

$2,000 + 3% on all sales
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.

Answer 1

Let S = sales (in dollars).

1) Salary + 3%: 3500 = 2000 + 0.03S → 1500 = 0.03S → S = 1500/0.03 = $50,000.

2) 7% straight commission: 3850 = 0.07S → S = 3850/0.07 = $55,000.

3) Graduated: 3600 = 0.05(40000) + 0.08(S − 40000) → 3600 = 2000 + 0.08(S − 40000)
→ 1600 = 0.08(S − 40000) → S − 40000 = 20000 → S = $60,000.

The graduated commission employee had the largest sales. Answer: c.