Question

a doctor prescribes an ointment that is 4% hy drocortisone. a pharmacist has 1 % and 5% concentrations in stock. how many ounces of each should the pharmacist use to make a 1-ounce tube

Answer 1

To make a 1-ounce tube of 4% hydrocortisone ointment, the pharmacist should use 1/4 ounce of the 1% concentration and 3/4 ounce of the 5% concentration.

Step-by-step explanation:

To find the amounts of 1% and 5% concentrations needed to make a 1-ounce tube of 4% hydrocortisone ointment, we can set up a system of equations.

Let x be the amount (in ounces) of the 1% concentration used, and let y be the amount (in ounces) of the 5% concentration used.

We know that the total amount of ointment is 1 ounce, so we have the equation:

x + y = 1

We also know that the amount of hydrocortisone in the ointment is 4% of the total amount, so we have the equation:

0.01x + 0.05y = 0.04(1)

Simplifying the second equation, we have:

0.01x + 0.05y = 0.04

Multiplying both sides by 100 to eliminate decimals, we get:

x + 5y = 4

Now we can solve the system of equations:

x + y = 1

x + 5y = 4

Multiplying the first equation by -1 and adding the two equations together, we can eliminate x:

-x - y = -1

x + 5y = 4

4y = 3

y = 3/4

Substituting y back into the first equation, we can solve for x:

x + (3/4) = 1

x = 1 - (3/4)

x = 1/4

So, the pharmacist should use 1/4 ounce of the 1% concentration and 3/4 ounce of the 5% concentration to make a 1-ounce tube of 4% hydrocortisone ointment.