Question

solve the proportion problems: (\frac{2}{5} = \frac{5}{x}) and (\frac{x - 10}{x} = \frac{x - 2}{5})

Explanation:

Step1: Solve first equation for $x$

Start with $\frac{2}{x} = \frac{5}{2}$. Cross-multiply to isolate $x$.
$5x = 2 \times 2$
$5x = 4$
$x = \frac{4}{5}$

Step2: Solve second equation for $x$

Start with $\frac{x-10}{2} = \frac{x-8}{5}$. Cross-multiply to eliminate denominators.
$5(x-10) = 2(x-8)$
$5x - 50 = 2x - 16$
$5x - 2x = 50 - 16$
$3x = 34$
$x = \frac{34}{3}$

Answer:

1. $x = \frac{4}{5}$
2. $x = \frac{34}{3}$