Question

A pharmacist needs to fill an order for a 3% lidocaine topical cream. However, only 2% and 4% concentrations are in Stock. How much of the 4% concentration should be mixed with 30 g of the 2% concentration to get a 3% concentration?

Answer 1

x = grams of 4% cream

0.04x + 0.02(30) = 0.03(30+x)
0.04x + 0.6 = 0.9 + 0.03x
0.04x - 0.03x = 0.9 - 0.6
0.01x = 0.3
x = 0.3/0.01
x = 30 grams

3% concentration is exactly inbetween 2%-4% so it makes sense that a 1/2 and 1/2 mixture of both would give 3% concentration.