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Math Help - Mixture Problem - Preparing eye drops

  1. #1
    Member Jonboy's Avatar
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    Mixture Problem - Preparing eye drops

    Hello everyone, this is my first post of asking assistance on this site. You know what they say... everyone needs someone sometime.

    Here's what I need help on:

    A pharmacist is to prepare 15 milliliters of special eye drops for a glaucoma [whatever that is lol] patient. The eye-drop solution must have a 2% 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?
    I got a feeling I'm making this problem way too ubereasy. I just said 1% solution of the 2% and 1% of 10% solution to give me 2% of a active ingredient. I got a feeling there's more here... but I don't see what.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Jonboy View Post
    Hello everyone, this is my first post of asking assistance on this site. You know what they say... everyone needs someone sometime.

    Here's what I need help on:

    I got a feeling I'm making this problem way too ubereasy. I just said 1% solution of the 2% and 1% of 10% solution to give me 2% of a active ingredient. I got a feeling there's more here... but I don't see what.
    For the record....

    Glaucoma is an eye disease where the pressure of the fluid in the interior of the eye is consistently too high. Several things happen if you have it for long enough: a decrease in peripheral vision, damage to the optic nerve, and pain are common in the advanced version. My father, for example, has had glaucoma for more than 30 years and is now effectively blind. (A stroke complicated things, but the glaucoma is what sealed the damage to the optic nerve.)

    If caught in the early stages there are medications that can help and laser surgery can lower pressures almost immediately. My Dad had a rather invasive procedure: they poked a hole in the side of his eye and put a "tube" in to keep the hole open to bleed the excess pressure off. (Don't worry, you can't see it.) It's too late for his sight, but at least the glaucoma isn't hurting him.

    Just thought I'd chip in the information.

    -Dan
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  3. #3
    Eater of Worlds
    galactus's Avatar
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    Hey Jonboy:

    Let x = the amount of solution to be at 10%.

    The 15-x is the amount at 1%

    So, we have 0.10x+0.01(15-x)=0.02(15)

    Solve for x.
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