Question

You receive an order for 30 grams of 0.1 percent hydrocortisone cream for use on an infant. You have available 1 percent hydrocortisone cream and cold cream that can be mixed with the hydrocortisone. How many grams of the cold cream will be needed to fill the order?

Answer 1

Order received = 30 grams of 0.1 % hydrocortisone cream.

Available concentration = 1% hydrocortisone cream.

The required amount of 1% hydrocortisone cream in the final product can be calculated by either of the following methods.

Method 1:

0.1% of 30 grams = 0.1/100 x 30 grams

= 0.03 grams.

Therefore, 0.3 grams of hydrocortisone is present in the final order.

Now, available product concentration = 1% of hydrocortisone cream.

This means, 1 gram of hydrocortisone is present in 100 grams of hydrocortisone cream.

Therefore, 0.03 gram of hydrocortisone is present in 0.03 x 100 grams of hydrocortisone cream

= 3 grams of hydrocortisone cream.

Method 2:

Alternatively, the required amount of 1% hydrocortisone cream can be calculated directly by the following formula,

C₁V₁ = C₂V₂

where, C₁ = Initial concentration of the product

V₁ = Initial volume of the product.

C₂ = Final concentration of the product

V₂ = Final volume of the product.

Now, since, Density = Mass/Volume.

Therefore, Volume = Mass/Density.

Replacing the volume by mass/density on both sides, we cancel out the density and hence we can rewrite the equation as,

Initial concentration x Initial mass = Final concentration x Final mass

Now, here, Initial concentration = 1%

  Final concentration = 0.1%

Final mass of the product = 30 gram

Therefore, 1% x Initial mass = 0.1% x 30 gram

Or, Initial mass = 0.1/1 x 30 gram

= 1/10 x 30 gram

= 3 grams.

Thus, required amount of 1% hydrocortisone cream to produce the final product of 0.1% concentration = 3 gram.

Since, the total mass of the final product is 30 grams, the remaining mass must be made up by cold cream.

Therefore, required amount of cold cream = 30 gm - 3 gm = 27 gm.

Hence, 27 grams of cold cream is needed to fill the order.