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.
How much is needed of each?
Let x = amount of the 0.025% (and it's easier if we just leave it in percent).
Then 180-x = amount of the 0.1%.
0.025x + (180-x)*0.1 = 180*0.05
Solve for x and 180-x
I've estimated this will be 120 of the 0.025% and 60 of the 0.1% to give 180 of 0.05% but you should confirm all of this.
To find out how much of each cream is needed to prepare 180 g of Lotrimin 0.05% cream, let's assign variables to the quantities we need to determine.
Let's say we need x grams of Lotrimin 0.025% cream and y grams of Lotrimin 0.1% cream.
Since the total quantity required is 180 g, we can set up the equation: x + y = 180.
Now let's set up another equation based on the active ingredient concentration:
For Lotrimin 0.025% cream, the amount of active ingredient is 0.025% of the total weight (x + y). Thus, the quantity of the active ingredient in this cream is (0.025/100) * (x + y) = 0.00025 * (x + y).
Similarly, for Lotrimin 0.1% cream, the quantity of the active ingredient is (0.1/100) * (x + y) = 0.001 * (x + y).
Now, according to the problem statement, we want to prepare 180 g of Lotrimin 0.05% cream. In this cream, the quantity of the active ingredient is (0.05/100) * 180 = 0.0005 * 180 = 0.09 g.
Since the total quantity of the active ingredient in both creams should add up to 0.09 g, we can set up the equation:
0.00025 * (x + y) + 0.001 * (x + y) = 0.09.
Now, let's solve the system of equations:
x + y = 180 (equation 1)
0.00025 * (x + y) + 0.001 * (x + y) = 0.09 (equation 2)
First, simplify equation 2:
0.00025 * (x + y) + 0.001 * (x + y) = 0.09
0.00125 * (x + y) = 0.09
(x + y) = 0.09 / 0.00125
(x + y) = 72
Now, substitute this value of (x + y) into equation 1:
x + y = 180
72 = 180 - y
y = 180 - 72
y = 108
Substituting the value of y back into equation 1:
x + 108 = 180
x = 180 - 108
x = 72
Therefore, to prepare 180 g of Lotrimin 0.05% cream, you will need 72 g of Lotrimin 0.025% cream and 108 g of Lotrimin 0.1% cream.