A pharmacist has a 6% solution of cough syrup and a 14% solution of the same cough syrup. How many ounces of each must be mixed to make 16 ounces of a 10% solution of cough syrup?
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Let a represent the amount of 6% solution of cough syrup and b represent the amount of 14% cough syrup.
The total amount of the final solution is 16 ounces.
a+b =16
The total solute in the final solution is:
0.06a + 0.14b =0.10(16)
0.06 (16 - b) + 0.14b = 1.6
0.96 - 0.06b + 0.14b = 1.6
0.08b = 0.64
b = 8
a = 16-8
= 8
8 ounces each of 6% and 14% solution of cough syrup must be combined.
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