A pharmacist is to prepare 15 milliliters of special eye drops for a glaucoma patient. The eye-drop solution must have a 7% active ingredient, but the pharmacist only has 10% solution and 1% solution in stock. How much of each type of solution should be used to fill the prescription?
If there are x mL of 10%, then the rest (15-x) are 1%
Now make sure the amount of active ingredient adds up right:
.10x + .01(15-x) = .07*15
solve for x
1
To prepare 15 milliliters of a 7% eye-drop solution using the 10% and 1% solutions, you need to determine the amount of each solution to use.
Let's assume X milliliters of the 10% solution and Y milliliters of the 1% solution will be used.
First, let's calculate the total amount of active ingredient in the desired solution:
Total Active Ingredient = 15 ml × 7% = 1.05 ml
Now, we can set up the equation based on the total amount of active ingredient:
0.1X + 0.01Y = 1.05
We also need to consider the total volume of the solution:
X + Y = 15
Now, we have a system of equations. We can solve this system using various methods, like substitution or elimination. Let's use the substitution method here:
From the second equation, we can rewrite X as X = 15 - Y.
Substituting this value into the first equation:
0.1(15 - Y) + 0.01Y = 1.05
Expanding and simplifying:
1.5 - 0.1Y + 0.01Y = 1.05
Combining like terms:
0.09Y = 1.05 - 1.5
0.09Y = -0.45
Dividing both sides by 0.09:
Y = -0.45 / 0.09
Y = 5
Now, substituting this value back into the second equation:
X + 5 = 15
X = 15 - 5
X = 10
Therefore, you would need 10 milliliters of the 10% solution and 5 milliliters of the 1% solution to prepare the 15 milliliters of a 7% eye-drop solution.
To determine how much of each type of solution should be used to fill the prescription, we can set up a system of equations. Let's represent the amount of 10% solution used as "x" milliliters, and the amount of 1% solution used as "y" milliliters.
1. Equation for the total volume of the solution:
x + y = 15
2. Equation for the total amount of active ingredient:
(0.10 * x) + (0.01 * y) = 0.07 * 15
Simplifying the second equation:
0.10x + 0.01y = 1.05
Now we can solve the system of equations using various methods. Let's use the method of substitution.
From the first equation, we have x = 15 - y. Substituting this value into the second equation:
0.10(15 - y) + 0.01y = 1.05
1.5 - 0.10y + 0.01y = 1.05
-0.09y = 1.05 - 1.5
-0.09y = -0.45
y = (-0.45)/(-0.09)
y = 5
Substituting the value of y back into the first equation:
x + 5 = 15
x = 15 - 5
x = 10
Therefore, the pharmacist should use 10 milliliters of the 10% solution and 5 milliliters of the 1% solution to prepare the 15 milliliters of special eye drops for the glaucoma patient.