A patient is receiving a drip of LRS + 2.5% dextrose. You need to increase the dextrose concentration to 5%. There are 837 ml left in the bag. How many ml of 50% dextrose do you need to add to increase the concentration to 5%? Give the exact answer and round your answer to the nearest ml (no decimals).

To solve this problem, we need to calculate the volume of 50% dextrose solution required to increase the concentration of dextrose in the remaining 837 mL of LRS + 2.5% dextrose solution to 5%.

### Step-by-step solution:

#### 1. Current amount of dextrose in the bag:
The current concentration of dextrose is 2.5%, which means there are 2.5 grams of dextrose per 100 mL of solution. For 837 mL, the total amount of dextrose is:

\[
\text{Current dextrose} = \frac{2.5}{100} \times 837 = 20.925 \, \text{grams}
\]

#### 2. Final concentration of dextrose (after adding 50% dextrose):
The desired concentration is 5%, so the total solution after adding the 50% dextrose should have 5 grams of dextrose per 100 mL of solution.

Let \( x \) be the volume of 50% dextrose solution to be added. The total volume of the solution after adding \( x \) mL of 50% dextrose will be \( 837 + x \) mL.

#### 3. Total amount of dextrose after adding the 50% dextrose:
- The amount of dextrose in \( x \) mL of 50% dextrose is \( 0.5x \) grams (since 50% dextrose contains 0.5 grams per mL).
- The total dextrose after adding will be \( 20.925 + 0.5x \) grams.

#### 4. Set up the equation:
To achieve the final concentration of 5%, the total amount of dextrose in the new solution should be:

\[
\frac{5}{100} \times (837 + x) = 20.925 + 0.5x
\]

Simplifying:

\[
0.05 \times (837 + x) = 20.925 + 0.5x
\]

\[
41.85 + 0.05x = 20.925 + 0.5x
\]

#### 5. Solve for \( x \):

\[
41.85 - 20.925 = 0.5x - 0.05x
\]

\[
20.925 = 0.45x
\]

\[
x = \frac{20.925}{0.45} = 46.5 \, \text{mL}
\]

#### 6. Round to the nearest mL:
The volume of 50% dextrose needed is approximately \( 47 \, \text{mL} \).

### Final answer: 
You need to add **47 mL** of 50% dextrose to the solution.

Would you like more details or have any questions? Here are some related questions you might find useful:

1. What happens if the dextrose concentration is too high or too low in a medical setting?
2. How do you calculate the dextrose concentration after mixing two solutions with different concentrations?
3. Why is dextrose often added to solutions like LRS in medical treatments?
4. What are other common concentrations of dextrose used in IV fluids?
5. Can we use the same approach for other solutes in IV fluids?

**Tip**: When dealing with IV fluids, always verify the total volume and concentration to ensure proper dosage adjustments!

Learn how to calculate the exact volume of 50% dextrose needed to increase the concentration of dextrose from 2.5% to 5% in an 837 mL IV solution. This problem involves concentration calculations, linear equations, and proportionality, and provides a step-by-step guide. Suitable for students in Grades 9-12 or introductory medical studies.

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