A pharmacist wants to mix an ointment that is 6% zinc oxide with an ointment that is 12% zinc oxide to make 30 grams of an ointment that is 10% zinc oxide. How many grams of each ointment should the pharmacist mix together? Can anyone breakdown this problem for me, so that I can learn how to do these types of problems. Thanks

Question

anonymous · Answer

Mixture problems are hard. Take it a step at a time. 
We know that the end product is .10 x (30)
The first ingredient  is .06 time some amount x, the second ingredient is .12 x (30 - x)
if we put it all together
$$.06x + .12(30 - x) = .10(30)$$
$$.06x + 3.6 - .12x = 3.0$$
$$-.06x + 3.6 = 3.0$$
$$-.06x = -0.6$$
$$x = 10$$
so we need 10 grams of the 6% and 20 grams of the 12%

anonymous · Answer

Thank you so much for helping me with my problem.