Kaplan GMAT Solution PS

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sparkles3144: Master | Next Rank: 500 Posts; Posts: 145; Joined: Fri Jan 18, 2013 8:27 am; Thanked: 7 times

by sparkles3144 » Fri Jul 19, 2013 6:25 pm

A pharmacist is mixing a medication for a patient by combining two solutions with different concentrations of active ingredient. The patient needs 5 milliliters of the active ingredient in each dose, and he needs 30 doses. Solution A is 5% the active ingredient by volume, and solution B is 20% the active ingredient by the volume. If the patient receives a total of 1000 milliliters of medication, how many milliliters of solution A did the pharmacist use in mixing the medication?

Please help me!

Thanks!

Source: Beat The GMAT — Problem Solving | Fri Jul 19, 2013 6:25 pm

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by [email protected] » Sat Jul 20, 2013 12:43 am

Hi sparkles3144,

This is an example of a mixture question that uses "system math" from algebra. Your job is to translate the sentences into equations and then use the equations to solve the problem:

First, the equations:

.05A + .2B = 150 This equation is for the active ingredients (5 ml x 30 doses = 150 ml of active ingredient)
A + B = 1000 This equation is for the total medication

Now you can solve using either substitution or combination to figure out the value of A.

B = 1000 - A

.05A + .2(1000 - A) = 150

50 = .15A

50/.15 = A

A = 1000/3

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