Question

solve the equation.
\\(\frac{8}{x} = \frac{40}{25}\\)

select the correct choice below and fill in any answer boxes present in your choice.
\\(\bigcirc\\) a. the solution is \\(x = \square\\).
(type an integer or a simplified fraction. use a comma to separate answers as needed.)
\\(\bigcirc\\) b. there is no solution.

Explanation:

Step1: Cross - multiply the equation

Given the equation \(\frac{8}{x}=\frac{40}{25}\), cross - multiplying (which is based on the property of proportions: if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d = b\times c\)) gives us \(8\times25=40\times x\).
Calculating the left - hand side: \(8\times25 = 200\), so the equation becomes \(200 = 40x\).

Step2: Solve for \(x\)

To solve for \(x\), we divide both sides of the equation \(200 = 40x\) by 40.
Using the division operation: \(x=\frac{200}{40}\).
Simplifying the fraction \(\frac{200}{40}\), we know that \(200\div40 = 5\).

Answer:

A. The solution is \(x = 5\)