Robert sells life insurance for a major insurance company for a commission. Last year he sold $12,000,000 worth of insurance. He earned $72,000 in commissions. What was his commission rate?

Question

Robert sells life insurance for a major insurance company for a commission.  Last year he sold $12,000,000 worth of insurance. He earned $72,000 in commissions. What was his commission rate?

Eli Assouline · Accepted Answer

The commission is 0.6% of sales

Using ratio: #("commission")/("sales") ->(72,000)/(12,000,000) = (72xxcancel(10^3))/(12xx10^3xxcancel(10^3))# #=" "72/12xx1/10^3" "=" "(72-:12)/(12-:12)xx1/10^3# #" "("commission")/("sales") " "=" "6/10^3 # '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Now it all depends on how you wish to express this. Expressed as percentage we need to convert this fraction so that the denominator (bottom number) is 100. Which is #10^2# We do this by applying #10^3-:10# but to maintain the ratio we also have to divide the top number (numerator) by 10 giving: #" "("commission")/("sales") " "=" "(6-:10)/(10^3-:10) " "=" "0.6/100 # #" "color(green)(ul(bar(|color(white)(2/2)" So the commission is 0.6% "|)))# #color(blue)("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~")# #color(blue)("Just for fun lets see how much would need to be sold to make $100,000 commission")# #0.6/100 x = $100,000# #=> x=100/0.6xx100000# #x=$16,666,666.67# to 2 decimal places

Robert sells life insurance for a major insurance company for a commission. Last year he sold $12,000,000 worth of insurance. He earned $72,000 in commissions. What was his commission rate?

Robert sells life insurance for a major insurance company for a commission. Last year he sold $12,000,000 worth of insurance. He earned $72,000 in commissions. What was his commission rate?