a pharmacist needs to mix a 5% anti cream with a 10% anti cream to make 50 mm of a mixture that contains 8% of the anti cream,. How much of the 5% cream and the 10% cream is needed

Answer 1

For these mixture problems, you need to focus on the quantity of the anti cream (whatever that is).

If x = the amount of 5% cream, then there is 0.05x of the active ingredient in x mm's. (Millimeters is a linear measure!!)

Also, for the 10% solution there will be 50 - x mm's of it in the final mixture, 0.10(50 - x) of the active ingredient.

So the equation is 0.05x + 0.10(50 - x) = 0.08(50)

0.05x + 5 - 0.10x = 4

-0.01x = -1 and x = -1/-0.01, or 20 mm's of the 5% and 50 - 20, or 30 mm's of the 10%.

Answer 2

You will need 20 millimetres of the 5% cream and 30 millimetres of the 10% cream in order to create a combination with 8% anti-cream that has a volume of 50 millimetres.