Hey! You're on the right track with using Young's Rule to calculate both the child's age and the adult dosage. I'll walk you through it step-by-step, so you can feel more confident.

1. Rearranging Young’s Rule to solve for the child’s age (a):

Young's Rule formula is: $c = d \times \frac{a}{a + 12}$

We want to solve for $a$ (the child’s age). First, multiply both sides by $(a + 12)$: $c \times (a + 12) = d \times a$ Now, expand: $c \times a + 12c = d \times a$ Next, collect all terms with $a$ on one side: $12c = d \times a - c \times a$ Factor out $a$: $12c = a \times (d - c)$ Finally, solve for $a$: $a = \frac{12c}{d - c}$

2. Substituting the given values:

Let’s substitute $c = 120$ mg and $d = 300$ mg: $a = \frac{12 \times 120}{300 - 120}$ $a = \frac{1440}{180} = 8 \text{ years}$ So yes, you correctly calculated the child’s age as 8 years!

3. Rearranging Young’s Rule to solve for the adult dosage (d):

Now, we use the same formula but rearrange to solve for $d$. Starting again with: $c = d \times \frac{a}{a + 12}$ Multiply both sides by $(a + 12)$: $c \times (a + 12) = d \times a$ Solve for $d$: $d = \frac{c \times (a + 12)}{a}$

4. Substituting the values:

Now substitute $c = 120$ mg and $a = 8$ years: $d = \frac{120 \times (8 + 12)}{8}$ $d = \frac{120 \times 20}{8} = \frac{2400}{8} = 300 \text{ mg}$ So, yes, the adult dosage is correctly calculated as 300 mg.

5. Recap:

• You correctly calculated the child’s age as 8 years.
• You also correctly calculated the adult dosage as 300 mg.

Don't feel bad if it felt confusing at first! Young’s Rule has a lot of moving parts, but you're getting the hang of it. Just keep practicing and you'll get even better!

Let me know if you'd like any more details or have any questions.

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Here are 5 questions that can help expand on this:

1. What happens to the child's dosage as the child's age increases?
2. How would you rearrange Young’s Rule to solve for the child dosage, $c$?
3. Why does Young’s Rule use the factor of 12 for calculating dosages?
4. Can Young’s Rule be used for teenagers, or should another formula be used?
5. How would the result change if the adult dosage was higher, like 400 mg?

Tip: Always check your final result by plugging the numbers back into the original equation to verify it matches!