Respond to this student as a student: 

The age is 30

Use the child dosage (c=120) mg and the adult dosage (d=300) mg to calculate the child's age (a)

Rearrange young's rule  formula to solve for (a)

a=cx 12d-ca=d-cc x12

Substituting the values

a=120x12300-120=1440180=8years a =300-120120x12 =1801440 =8 years

Verify that the child's age matches the provided age of 8 years.

Use the child dosage(c=120)mg and the child's age (a=8) years to calculate the adult dosage (d)

rearrange young's rule formula to solve for (d)

d=cx(a+12) ad=ac x(a+12)

Substituting the values:

d=120 x(8+12)8= 120x208=24008 =300mgd=8120x(8+12) =8120x20+82400=300mg

verify that the adult dosage matches the provided adult dosage of 300 mg.

If anyone has any help on this problem please send your feed back because I felt very lost in this. I had to ask for a lot of help trying to figure things one out. I just hope that I got this one right.

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.

---

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!

Respond to this student as a student: The age is 30. Use the child dosage (c=120) mg and the adult dosage (d=300) mg to calculate the child's age (a). Rearrange Young's Rule formula to solve for (a). a=cx 12d-ca=d-cc x12. Substituting the values a=120x12300-120=1440180=8years a =300-120120x12 =1801440 =8 years. Verify that the child's age matches the provided age of 8 years. Use the child dosage (c=120) mg and the child's age (a=8) years to calculate the adult dosage (d). Rearrange Young's Rule formula to solve for (d). d=cx(a+12) ad=ac x(a+12). Substituting the values: d=120 x(8+12)8= 120x208=24008 =300mgd=8120x(8+12) =8120x20+82400=300mg. Verify that the adult dosage matches the provided adult dosage of 300 mg.

Learn how to use Young's Rule to calculate a child's age from dosage and verify it against the provided values. Step-by-step guidance on rearranging the formula to solve for both the child's age and adult dosage, with examples and key mathematical concepts. Suitable for students in Grades 9-10.

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