Prepare 180 g of Lotrimin 0.05% cream. In stock, you have 200 g each of Lotrimin 0.025% cream and Lotrimin 0.1% cream
To prepare 180 g of Lotrimin 0.05% cream, you would need to calculate the amounts of the two available creams that should be combined.
First, let's determine how much of the 0.025% cream and the 0.1% cream is required.
1. Calculate the total amount of cream needed:
Total Amount = 180 g
2. Determine the amount and concentration of the first cream:
Cream 1: Lotrimin 0.025% cream
Amount of Cream 1 = x (grams)
3. Determine the amount and concentration of the second cream:
Cream 2: Lotrimin 0.1% cream
Amount of Cream 2 = 180 - x (grams)
Next, let's set up an equation based on the percentage of the active ingredient in each cream.
1. Set up an equation using the concentration of the active ingredient (0.05%):
(0.025% * Amount of Cream 1) + (0.1% * Amount of Cream 2) = 0.05% * 180 g
2. Simplify the equation:
(0.025/100 * Amount of Cream 1) + (0.1/100 * Amount of Cream 2) = 0.05 * 180 g
Now, let's solve the equation to find the amount of each cream needed:
1. Substitute the value of Amount of Cream 2 from step 3 into the equation:
(0.025/100 * Amount of Cream 1) + (0.1/100 * (180 - Amount of Cream 1)) = 0.05 * 180 g
2. Solve for Amount of Cream 1:
0.025/100 * Amount of Cream 1 + 0.1/100 * (180 - Amount of Cream 1) = 0.05 * 180 g
0.025/100 * Amount of Cream 1 + 0.018 - 0.001/100 * Amount of Cream 1 = 9
0.025 * Amount of Cream 1 + 0.018 - 0.001 * Amount of Cream 1 = 90
0.024 * Amount of Cream 1 = 89.982
Amount of Cream 1 ≈ 3749.25 g
3. Calculate the Amount of Cream 2:
Amount of Cream 2 = 180 - Amount of Cream 1
Amount of Cream 2 ≈ 180 - 3749.25 g
Amount of Cream 2 ≈ -3569.25 g
Since the amount of Cream 2 is negative, it means that there is not enough Lotrimin 0.025% cream in stock to prepare the desired formulation of 180 g Lotrimin 0.05% cream.