gistfile1.txt

A prescription calls for 50 g of a 10 % ointment. The pharmacist only
has a 5 % ointment and the pure ingredient available. How much of
the 5 % ointment and the pure ingredient are needed to compound
the prescription?

Let x be the amount of 5% ointment
Let y be the amount of 100% ointment

x * 5% ointment + y * 100% ointment = 50g of 10% ointment

Given that the maximum amount of ointment is 50g
Let y = 50 - x

x * 5% ointment + (50 - x) * 100% ointment = 50g 10% ointment

x * 0.05 + (50 - x) * 1.00 = 50 * 0.10
0.05x + (50 - x) = 5
0.05x + 50 - x = 5
50 - 0.95x = 5
45 - 0.95x = 0
45 = 0.95x
x = 45 / 0.95
x = 47.368~

Solve for y:

y = 50 - x
y = 50 - 47.368~
y = 2.632~

Solution: It takes 47.368g of 5% ointment, 2.632g of 100% ointment to make 50g of 10% ointment.

Also I'm a huge nerd.

http://www.wolfram.com/mathematica/

Yeah, but I wanted to show working. And the EULA of it forbids any Asians from using it because they don't want a huge deluge of math related bug reports. Which are actually bugs.