MATH SOLVE

3 months ago

Q:
# A cold tablet contains the following amounts of active ingredients: acetaminophen 325 mg, chlorpheniramine maleate 2 mg, and dextromethorphan 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?

Accepted Solution

A:

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:[tex]325 mg + 2mg+15 mg=342 mg[/tex]The percentages of each component in the formula are:Acetaminophen:[tex]\frac{325mg*100}{342mg}=95.03[/tex]%Chlorpheniramine maleate:[tex]\frac{2mg*100}{342mg} =0.58[/tex]%Dextromethorphan hydrobromide:[tex]\frac{15mg*100}{342mg}=4.39[/tex]%If 1 Kg=[tex]10^{6}[/tex] mg of acetaminophen is used, the needed amount of chlorpheniramine maleate would be:[tex]\frac{10^{6} mg *0.58}{95.03}=6153.85 mg[/tex]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:[tex]\frac{10^{6}mg*100}{95.03}=1052307.7mg[/tex]Since each tablet weighs 342 mg, the number of tablets that can be prepared is:[tex]\frac{1052307.7mg}{342mg}=3076.923[/tex]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.