If `a/b = c/d =e/f = 4,` then
`( ma + nc + pe )/( mb + nd + pf) = ?`

Options

A. 1
B. 2
C. 3
D. 4

Answer

To solve the problem, we start with the given ratios:

1. **Given Ratios**:
\[ \frac{a}{b} = \frac{c}{d} = \frac{e}{f} = 4 \]

2. **Express Variables in Terms of Others**:
- From \(\frac{a}{b} = 4\), we can express \(a\) in terms of \(b\):
\[ a = 4b \]
- From \(\frac{c}{d} = 4\), we can express \(c\) in terms of \(d\):
\[ c = 4d \]
- From \(\frac{e}{f} = 4\), we can express \(e\) in terms of \(f\):
\[ e = 4f \]

3. **Substituting into the Expression**:
We need to evaluate:
\[ \frac{ma + nc + pe}{mb + nd + pf} \]
Substituting the expressions for \(a\), \(c\), and \(e\):
\[ = \frac{m(4b) + n(4d) + p(4f)}{mb + nd + pf} \]
Simplifying the numerator:
\[ = \frac{4mb + 4nd + 4pf}{mb + nd + pf} \]

4. **Factoring Out the Common Factor**:
We can factor out 4 from the numerator:
\[ = \frac{4(mb + nd + pf)}{mb + nd + pf} \]

5. **Final Simplification**:
Since \(mb + nd + pf\) is common in both the numerator and the denominator, we can cancel it out (assuming \(mb + nd + pf \neq 0\)):
\[ = 4 \]

Thus, the final answer is:
\[ \frac{ma + nc + pe}{mb + nd + pf} = 4 \]