Question

how many grams of 2.5% and 10% hydrocortisone (hydrocort) cream are needed to prepare 15 g of a 5% hydrocortisone cream?

7.5 g of 10% hydrocortisone cream and 7.5 g of 2.5% hydrocortisone cream

2 g of 10% hydrocortisone cream and 8 g of 2.5% hydrocortisone cream

10 g of 10% hydrocortisone cream and 5 g of 2.5% hydrocortisone cream

5 g of 10% hydrocortisone cream and 10 g of 2.5% hydrocortisone cream

Explanation:

Step1: Let the amount of 10% hydrocortisone cream be $x$ grams.

Then the amount of 2.5% hydrocortisone cream is $(15 - x)$ grams.

Step2: Set up an equation based on the amount of hydrocortisone in each cream.

The amount of hydrocortisone in the 10% cream is $0.1x$, the amount in the 2.5% cream is $0.025(15 - x)$, and the amount in the final 5% cream is $0.05\times15$. So the equation is $0.1x+0.025(15 - x)=0.05\times15$.

Step3: Expand and simplify the equation.

$0.1x + 0.375-0.025x=0.75$. Combine like - terms: $0.1x-0.025x=0.75 - 0.375$. So $0.075x=0.375$.

Step4: Solve for $x$.

$x=\frac{0.375}{0.075}=5$ grams (amount of 10% hydrocortisone cream).

Step5: Find the amount of 2.5% hydrocortisone cream.

$15 - x=15 - 5 = 10$ grams.

Answer:

5 g of 10% hydrocortisone cream and 10 g of 2.5% hydrocortisone cream