Question

I need help with a concentration question. I need to know how to calculate the product with the higher concentration. $6.50 for 185 mL and the concentration of the active ingredient is 0.005% OR $7.00 for 165mL and the concentration of the active ingredient is 0.700%.

I need to know how to write this out so I can solve others like it..If anyone can help, it would be greatly appreciated.

Answer 1

Your question isn't quite clear. If you really DO want the product with the higher concn, it MUST be the 0.700%. Obviously 0.700% is a higher concn than 0.005% and there is no calculation to it. However, I suspect you really want the price per gram of each. Here is how you do that (and I'm assuming the concn quote is percent w/v and not w/w.
grams active ingredient in the first one is
(0.005 g/100 mL) x 185 mL = 0.00925 g.
That costs $6.50 so the price per gram is $6.50/0.00925 g = $702.70/gram.

The price of the other one per gram can be done exactly the same way. I obtained about $6.00/gram (but that isn't the exact answer) so the first one is much more expensive than the latter.

Answer 2

Thank you Dr. Bob. You were correct in your assumption. I had been staring at that problem for too long...It's very simple now that I see your solution. Thanks again for your help!