Question

The variables x and y vary inversely. Use the given values to write an equation that relates x and y. $$x=30, y=7.5$$

Short answer

The equation that represents the inverse variation between x and y is \(xy = 225\).

Step-by-step solution

Understanding the inverse relationship

In an inverse variation, the product of the two variables is a constant, i.e., \(xy = k\), where k is a constant.

Substitute the given values into the equation

Substitute \(x = 30\) and \(y = 7.5\) into the equation \(xy = k\), to find the value of k. The equation will be \(xy = 30 * 7.5\).

Solve for k

Solving the equation \(30 * 7.5 = k\) we get \(k = 225\).

Write the final equation

Substitute the value of k in the original equation. The final inverse variation equation will be \(xy = 225\).