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.