Question: As a nurse, part of your daily duties is to mix medications in the
proper proportions for your patients. For one of your regular
patients, you always mix Medication A with Medication B in the
same proportion. Last week, your patient's doctor indicated that
you should mix 60 milligrams of Medication A with 24 milligrams
of Medication B. However this week, the doctor said to only use 8 milligrams of Medication B. How many milligrams of Medication A should be mixed this week?
1. **State the problem:**
We need to find how many milligrams of Medication A should be mixed when Medication B is 8 milligrams, given the original proportion of 60 mg Medication A to 24 mg Medication B.
2. **Write the proportion formula:**
The ratio of Medication A to Medication B remains constant:
$$\frac{\text{Medication A}}{\text{Medication B}} = \frac{60}{24}$$
3. **Set up the equation for the new amount of Medication A ($x$):**
$$\frac{x}{8} = \frac{60}{24}$$
4. **Solve for $x$ by cross-multiplying:**
$$24 \times x = 60 \times 8$$
5. **Calculate the right side:**
$$24x = 480$$
6. **Divide both sides by 24 to isolate $x$:**
$$x = \frac{480}{24}$$
7. **Simplify the fraction by canceling common factors:**
$$x = \frac{\cancel{480}^{20} \times 24}{\cancel{24}} = 20$$
8. **Interpret the result:**
You should mix 20 milligrams of Medication A when using 8 milligrams of Medication B to maintain the same proportion.
**Final answer:**
$$\boxed{20}$$ milligrams of Medication A.