Math / Numbers & Operations

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A medication comes as a powder in a vial with 1 g of the active ingredient. The instructions say to reconstitute the powder with 20 mL of sterile water to make a final concentration of $50 \mathrm{mg} / \mathrm{mL}$ . The doctor orders 150 mg for the patient. How many mL will you administer per dose? (1) mL
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3 Answers 1 - 1 1.

Studdy Solution

STEP 1

What is this asking? How many milliliters of a reconstituted medication should be given to a patient if the doctor ordered 150 mg, and the reconstituted medication has a concentration of 50 mg/mL? Watch out! Don't get tripped up by the extra information about the 1g of active ingredient and the 20 mL of sterile water.
We only need the final concentration and the doctor's order.

STEP 2

1. Calculate the required volume.

STEP 3

Alright, future doctors and nurses, let's break this down!
We know the doctor ordered a dose of $150 \text{ mg}$ , and our reconstituted medication has a concentration of $50 \text{ mg/mL}$ .
We want to find the volume (in mL) to administer.
The relationship between these is:
$\text{Dose} = \text{Concentration} \cdot \text{Volume}$

STEP 4

Let's plug in what we know!
Our Dose is $150 \text{ mg}$ and our Concentration is $50 \text{ mg/mL}$ :
$150 \text{ mg} = 50 \text{ mg/mL} \cdot \text{Volume}$

STEP 5

Now, to find the Volume, we need to divide both sides of the equation by the Concentration, which is $50 \text{ mg/mL}$ :
$\text{Volume} = \frac{150 \text{ mg}}{50 \text{ mg/mL}}$

STEP 6

Notice how the mg units cancel out, leaving us with mL, which is exactly what we want!
$\text{Volume} = \frac{150}{50} \text{ mL}$ $\text{Volume} = 3 \text{ mL}$ So, we need to administer 3 mL of the reconstituted medication.

STEP 7

The required volume to administer is 3 mL.

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Studdy Solution

STEP 1

STEP 2

1. Calculate the required volume.

STEP 3

STEP 4

Let's plug in what we know!
Our Dose is $150 \text{ mg}$ and our Concentration is $50 \text{ mg/mL}$ :
$150 \text{ mg} = 50 \text{ mg/mL} \cdot \text{Volume}$

STEP 5

Now, to find the Volume, we need to divide both sides of the equation by the Concentration, which is $50 \text{ mg/mL}$ :
$\text{Volume} = \frac{150 \text{ mg}}{50 \text{ mg/mL}}$

STEP 6

Notice how the mg units cancel out, leaving us with mL, which is exactly what we want!
$\text{Volume} = \frac{150}{50} \text{ mL}$ $\text{Volume} = 3 \text{ mL}$ So, we need to administer 3 mL of the reconstituted medication.

STEP 7

The required volume to administer is 3 mL.

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Studdy Solution

STEP 1

STEP 2

1. Calculate the required volume.

STEP 3

STEP 4

Let's plug in what we know!Our **Dose** is 150 mg150 \text{ mg}150 mg and our **Concentration** is 50 mg/mL50 \text{ mg/mL}50 mg/mL:150 mg=50 mg/mL⋅Volume 150 \text{ mg} = 50 \text{ mg/mL} \cdot \text{Volume} 150 mg=50 mg/mL⋅Volume

STEP 5

Now, to find the **Volume**, we need to divide both sides of the equation by the **Concentration**, which is 50 mg/mL50 \text{ mg/mL}50 mg/mL:Volume=150 mg50 mg/mL \text{Volume} = \frac{150 \text{ mg}}{50 \text{ mg/mL}} Volume=50 mg/mL150 mg​

STEP 6

Notice how the *mg* units cancel out, leaving us with mL, which is exactly what we want!Volume=15050 mL \text{Volume} = \frac{150}{50} \text{ mL} Volume=50150​ mLVolume=3 mL \text{Volume} = 3 \text{ mL} Volume=3 mLSo, we need to administer **3 mL** of the reconstituted medication.

STEP 7

The required volume to administer is **3 mL**.

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Let's plug in what we know!
Our Dose is $150 \text{ mg}$ and our Concentration is $50 \text{ mg/mL}$ :
$150 \text{ mg} = 50 \text{ mg/mL} \cdot \text{Volume}$

Now, to find the Volume, we need to divide both sides of the equation by the Concentration, which is $50 \text{ mg/mL}$ :
$\text{Volume} = \frac{150 \text{ mg}}{50 \text{ mg/mL}}$

Notice how the mg units cancel out, leaving us with mL, which is exactly what we want!
$\text{Volume} = \frac{150}{50} \text{ mL}$ $\text{Volume} = 3 \text{ mL}$ So, we need to administer 3 mL of the reconstituted medication.

The required volume to administer is 3 mL.