If the recommended adult dosage for a drug is D , in milligrams, then to determine the appropriate dosage c for a child of a age a, where a > 1 , pharmacists use the equation c =0.0417D(a+1). The formula , rewritten to express a in terms of c and D , is

Options

A. `a=(c-1)/"0.0417D"`
B. `a=c/"0.0417D"-1`
C. a=0.0417D(c+1)
D. a=0.0417D(c-1)

Answer

To express the age \( a \) in terms of the child dosage \( c \) and the adult dosage \( D \) from the equation \( c = 0.0417D(a + 1) \), we can follow these steps:

### Step-by-step Solution:

1. **Start with the given equation**:
\[ c = 0.0417D(a + 1) \]

2. **Divide both sides by \( 0.0417D \)**:
To isolate \( a + 1 \), we divide both sides of the equation by \( 0.0417D \):
\[ \frac{c}{0.0417D} = a + 1 \]

3. **Subtract 1 from both sides**:
To solve for \( a \), we need to subtract 1 from both sides:
\[ a = \frac{c}{0.0417D} - 1 \]

4. **Final expression**:
Thus, the formula rewritten to express \( a \) in terms of \( c \) and \( D \) is:
\[ a = \frac{c}{0.0417D} - 1 \]