Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10. y varies jointly as x and z. y = 25 when x = 2 and z = 5. Find y when x = 8 and z = 12.

Key Concepts

Joint Variation

Joint variation occurs when a variable depends on two or more other variables. In this case, y varies jointly as x and z, meaning that y is proportional to the product of x and z. The relationship can be expressed mathematically as y = kxz, where k is a constant of variation.

Finding the Constant of Variation

To solve joint variation problems, the first step is to determine the constant of variation (k). This is done by substituting the known values of y, x, and z into the joint variation equation. For example, using y = 25, x = 2, and z = 5, we can solve for k to establish the relationship between the variables.

Substituting Values

Once the constant of variation is found, the next step is to substitute the new values of x and z into the equation to find the corresponding value of y. This involves using the established equation y = kxz with the new values to calculate y, demonstrating how changes in x and z affect y in joint variation.