Question

solve the proportion.
\\(\frac{35}{k} = \frac{7}{3}\\)
\\(k = \square\\)

Explanation:

Step1: Cross - multiply the proportion

To solve the proportion \(\frac{35}{k}=\frac{7}{3}\), we use the cross - multiplication property of proportions. If \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d = b\times c\).
Applying this to our proportion, we get \(35\times3=k\times7\).

Step2: Simplify both sides of the equation

First, calculate the left - hand side: \(35\times3 = 105\). So our equation becomes \(105 = 7k\).

Step3: Solve for \(k\)

To isolate \(k\), we divide both sides of the equation \(105 = 7k\) by 7.
\(k=\frac{105}{7}\)
Simplifying \(\frac{105}{7}\), we get \(k = 15\).

Answer:

\(15\)