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mr_godi [17]
3 years ago
10

A cold tablet contains the following amounts of active ingredients: acetaminophen 325 mg, chlorpheniramine maleate 2 mg, and dex

tromethorphan hydrobromide 15 mg. How many tablets may be prepared if a manufacturing pharmacist has 1 kg of acetaminophen, 125 g of chlorpheniramine maleate, and unlimited quantities of dextromethorphan hydrobromide?
Mathematics
1 answer:
kakasveta [241]3 years ago
7 0

Answer:

The number of tablets that can be prepared is 3076.

Step-by-step explanation:

The total amount of active ingredients in the tablet is the sum of the amounts provided in the formula:

325 mg + 2mg+15 mg=342 mg

The percentages of each component in the formula are:

Acetaminophen:\frac{325mg*100}{342mg}=95.03%

Chlorpheniramine maleate:\frac{2mg*100}{342mg} =0.58%

Dextromethorphan hydrobromide:\frac{15mg*100}{342mg}=4.39%

If 1 Kg=10^{6} mg of acetaminophen is used, the needed amount of chlorpheniramine maleate would be:

\frac{10^{6} mg *0.58}{95.03}=6153.85 mg

Since there are 125 g = 125000 mg of chlorpheniramine maleate, there is enough of these ingredient to run the available acetaminophen out. Thus, the total amount of active ingredients that can be prepared with 1 kg of acetaminophen is:

\frac{10^{6}mg*100}{95.03}=1052307.7mg

Since each tablet weighs 342 mg, the number of tablets that can be prepared is:

\frac{1052307.7mg}{342mg}=3076.923

Which means that 3076 tablets can be prepared and a there will be a remanent of 0.923*342 mg = 315.69 mg of active ingredients.

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