Solving a Word Problem: Preparing Special Eye Drops

[Zed]

Word problem !

Hi ,

This is a Hw question i have am stuck on i don't know how to solve it ...

A pharmacist is to prepare 16 milliliters of special eye drops for a glaucoma patient. The eye-drop solution must have a 5% active ingredient, but the pharmacist only has 10% solution and 1% solution in stock.


How much of 10% solution should be used to fill the prescription?

How much of 1% solution should be used to fill the prescription?


please help

thx

 

[Alkatran]

convert to formulas:
The amount of active solution in each ingredient should sum to the total active solution:
x*.1 + y*.01 = 16*.05
The amount of each ingredition should sum to the total amount:
x + y = 16

Then solve.

 

[quicknote]

Hello,

Thank you for reaching out for help with your word problem. I am happy to assist you in finding a solution.

To solve this problem, we need to use a mathematical approach called "mixture problems." This involves finding the right combination of two solutions with different concentrations to create a new solution with the desired concentration.

First, let's determine the amount of the 10% solution needed. We know that the final volume of the eye drops is 16 milliliters, and we want a 5% concentration of the active ingredient. This means that we need 5% of 16 milliliters to be the active ingredient, which is 0.8 milliliters.

Next, we need to figure out how much of the 10% solution contains 0.8 milliliters of the active ingredient. Since 10% of the 10% solution is the active ingredient, we can set up the following equation: 10% x Volume of 10% solution = 0.8 milliliters. Solving for the volume, we get 0.8 milliliters / 10% = 8 milliliters.

Therefore, we need 8 milliliters of the 10% solution to have 0.8 milliliters of the active ingredient in our final solution.

Now, for the 1% solution, we can use the same approach. We need to find out how much of the 1% solution contains 0.8 milliliters of the active ingredient. Setting up the equation, we get 1% x Volume of 1% solution = 0.8 milliliters. Solving for the volume, we get 0.8 milliliters / 1% = 80 milliliters.

So, we need 80 milliliters of the 1% solution to have 0.8 milliliters of the active ingredient in our final solution.

To summarize, you will need to use 8 milliliters of the 10% solution and 80 milliliters of the 1% solution to prepare 16 milliliters of special eye drops with a 5% concentration of the active ingredient.

I hope this helps you solve your word problem. Keep up the good work!

Best,

Scientist