Question

3
if \\(\frac{5a}{b} = 3.5\\) and \\(\frac{a}{bn} = 17.5\\), what is the value of \\(\frac{1}{n}\\)?

Explanation:

Step1: Analyze the given equations

We have two equations: \(\frac{5a}{b} = 3.5\) and \(\frac{a}{bn}=17.5\). Let's denote the first equation as Equation (1) and the second as Equation (2).

Step2: Divide Equation (1) by Equation (2)

Dividing \(\frac{5a}{b}\) by \(\frac{a}{bn}\) gives \(\frac{\frac{5a}{b}}{\frac{a}{bn}}\). When dividing by a fraction, we multiply by its reciprocal, so this becomes \(\frac{5a}{b}\times\frac{bn}{a}\). The \(a\) and \(b\) terms cancel out (assuming \(a
eq0\) and \(b
eq0\)), leaving \(5n\).

On the right - hand side, we divide \(3.5\) by \(17.5\). So we have the equation \(5n=\frac{3.5}{17.5}\).

Step3: Solve for \(n\)

First, calculate \(\frac{3.5}{17.5}\). We can rewrite this as \(\frac{3.5\div3.5}{17.5\div3.5}=\frac{1}{5} = 0.2\). So our equation is \(5n = 0.2\). Then, solve for \(n\) by dividing both sides by \(5\): \(n=\frac{0.2}{5}=0.04\).

Step4: Find the value of \(\frac{1}{n}\)

If \(n = 0.04\), then \(\frac{1}{n}=\frac{1}{0.04}\). We know that \(0.04=\frac{4}{100}=\frac{1}{25}\), so \(\frac{1}{n}=\frac{1}{\frac{1}{25}} = 25\).

Answer:

\(25\)