Solving Proportions: Find the Value of x

The problem presents a proportion involving an unknown value, $x$:

$1.75 : x :: 5 : 8$

This notation means that the ratio of 1.75 to $x$ is equivalent to the ratio of 5 to 8.

Proportion Equation Setup

We can express this proportion as an equation of fractions:

$ \frac{1.75}{x} = \frac{5}{8} $

Step-by-Step Calculation

1. Apply the cross-multiplication rule for proportions. Multiply the first term by the fourth term and set it equal to the product of the second term and the third term:

   $ 1.75 \times 8 = 5 \times x $

2. Calculate the product on the left side of the equation:

   $ 14 = 5x $

3. To find the value of $x$, divide both sides of the equation by 5:

   $ x = \frac{14}{5} $

4. Perform the division:

   $ x = 2.8 $

Result

The value of $x$ that satisfies the proportion is 2.8.