Quandaries and Queries

Name: Chet Warfel

Who is asking: Other
Level: All

My salesman calculates a customers profit margin by dividing what the customer paid by what he sells for, then subtracting that answer from 1. For example a customer sells a product for $15. He bought it for $10. 15/10=.66 Subtract that from 1 and get a profit % of 33%

Here's my question: If I want to figure what a reseller will sell a product for if he wants 40% margin(by the technique above), what formula do I use? Let's say I want to sell a product for 8.50, and I want the reseller to make 40%

My best technique is "guess and check" by plugging in the numbers and seeing if I'm too high or too low, then trying again. If I just multiply by 1.4 ....well that doesn't work! Help!

Thanks in advance.

Hi Chet,

I like this question, it shows the power of some algebra. First there is a typo in the question, to get the 0.66 above you should have said 10/15.

I need to introduce some letters to explain what to do. Suppose that the customer bought the item for $b and he sold it for $s. Your salesman calculates the profit margin (I will call it m) by

m = 1 - b/s In your example b = 10, s = 15 and m = 1 - 10/15 = 1 - 2/31/3 and 1/3 is 33%

Your question is then, if you know m and b, what is s? This is where you need some algebra. If

m = 1 - b/s then  b/s = 1 - m and hence s = b/1 - m In the example you give m = 40% = 0.40 and b = $8.50, so s = b/1 - m8.50/1 - 0.4 = $14.17


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