The pharmacist needs to measure out 35 grams of a 70% powder using the 50% and 90% powders he has in stock. how much of each powder is required?

let us say that:

x = mass of 50% powder

y = mass of 90% powder

eqtn 1 overall mass balance: x + y = 35

eqtn 2 poweder balance: 0.50 x + 0.90 y = 0.70 * 35 = > 0.50 x + 0.90 y = 24.5

Combining equations 1 and 2:

0.50 (35 - y) + 0.90 y = 24.5

17.5 - 0.50 y + 0.90 y = 24.5

0.40 y = 7

y = 17.5 grams

x = 35 - y = 35 - 17.5 = 17.5 grams

So equal amounts of 17.5 grams each are needed.

The pharmacist needs to measure out 17.5 grams of the 50% powder and 17.5 grams of the 90% powder and should end up with 35 grams of the 70% powder thus making for an easy method of calculation for mixing the two powders.