An insurance salesperson earns a commission of 3% of the first 5000 dollars on insurance that he sells each week and 4 percent of the value in excess of 5000 dollars. One week he earned a commission of 320 dollars. What was the total value of the insurance that he sold during the week?
0.03*5000 + 0.04(N-5000) = 320.
150 + 0.04N - 200 = 320,
0.04N = 370,
N = $9250 = Total sales.
To find the total value of insurance that the salesperson sold during the week, we need to use the given commission rate and amount earned.
Let's break down the commission calculation into two parts:
1. Calculate the commission earned on the first $5000 of insurance sold using a 3% commission rate.
2. Calculate the commission earned on the remaining amount of insurance sold above $5000 using a 4% commission rate.
Let's proceed with the calculations:
1. Commission on the first $5000:
The commission rate on the first $5000 is 3%. Therefore,
Commission on the first $5000 = 3% of $5000
= (3/100) * $5000
= $150
2. Commission on the excess amount:
The remaining commission is $320 - $150 (commission on the first $5000).
Therefore, commission on the excess amount = $320 - $150
= $170
To find the excess insurance value corresponding to this commission, we need to inverse the commission rate (4%) to get the multiplier. Since 4% is equivalent to 0.04, the multiplier is calculated as:
Multiplier = 1/0.04
= 25
Now, to find the total value of the insurance sold:
Total value of the insurance sold = Excess commission / Excess commission rate multiplier
= $170 / 25
= $6800
Therefore, the salesperson sold insurance totaling $6800 during the week.