Question

q1. a physician orders 225 mcg of a drug in liquid form. only a vial of this drug with a strength of 100 mcg/ml is on - hand. how many cubic centimeters should be extracted from the vial for the patient?

Explanation:

1. Explanation:

• We know that the desired strength of the drug is \(100\ mcg\) and the available drug has a strength of \(225\ mg\) in a certain volume (but we are interested in the ratio for extraction). First, we need to convert the units so that they are the same. Since \(1\ mg = 1000\ mcg\), then \(225\ mg=225\times1000 = 225000\ mcg\).
• Let \(x\) be the volume (in cubic - centimeters) to be extracted. We set up a proportion based on the concentration of the drug. The concentration of the available drug is \(\frac{225000\ mcg}{V}\) (where \(V\) is the total volume of the liquid - form drug, but we don't need to know \(V\) explicitly for the proportion). If we assume a linear relationship between the amount of drug and volume, we have the proportion \(\frac{225000\ mcg}{1\ cc}=\frac{100\ mcg}{x}\) (assuming the concentration is uniform and \(1\ cc\) is a reference volume for the available drug).
• Cross - multiplying gives us \(225000x = 100\times1\).
• Then we solve for \(x\) by dividing both sides of the equation by \(225000\).

Step 1: Set up the proportion

$$ \frac{225000}{1}=\frac{100}{x}$$

Step 2: Cross - multiply

$$225000x = 100$$

Step 3: Solve for \(x\)

$$x=\frac{100}{225000}=\frac{1}{2250}\approx0.000444\ cc$$

1. Answer:

\(\frac{1}{2250}\ cc\) (or approximately \(0.000444\ cc\))

Answer:

1. Explanation:

• We know that the desired strength of the drug is \(100\ mcg\) and the available drug has a strength of \(225\ mg\) in a certain volume (but we are interested in the ratio for extraction). First, we need to convert the units so that they are the same. Since \(1\ mg = 1000\ mcg\), then \(225\ mg=225\times1000 = 225000\ mcg\).
• Let \(x\) be the volume (in cubic - centimeters) to be extracted. We set up a proportion based on the concentration of the drug. The concentration of the available drug is \(\frac{225000\ mcg}{V}\) (where \(V\) is the total volume of the liquid - form drug, but we don't need to know \(V\) explicitly for the proportion). If we assume a linear relationship between the amount of drug and volume, we have the proportion \(\frac{225000\ mcg}{1\ cc}=\frac{100\ mcg}{x}\) (assuming the concentration is uniform and \(1\ cc\) is a reference volume for the available drug).
• Cross - multiplying gives us \(225000x = 100\times1\).
• Then we solve for \(x\) by dividing both sides of the equation by \(225000\).

Step 1: Set up the proportion

$$ \frac{225000}{1}=\frac{100}{x}$$

Step 2: Cross - multiply

$$225000x = 100$$

Step 3: Solve for \(x\)

$$x=\frac{100}{225000}=\frac{1}{2250}\approx0.000444\ cc$$

1. Answer:

\(\frac{1}{2250}\ cc\) (or approximately \(0.000444\ cc\))