Understanding Joint and Combined Variation

What is Joint Variation?

Joint variation occurs when a quantity varies directly as the product of two or more other quantities. If z varies jointly as x and y, it can be expressed as:

$$z = kxy$$

where k is the constant of variation.

What is Combined Variation?

Combined variation involves a combination of direct and inverse variation. For example, if z varies directly as x and inversely as y, it can be expressed as:

$$z = \frac{kx}{y}$$

where k is the constant of variation.

Examples of Joint and Combined Variation

• Joint Variation: If z varies jointly as x and y, and z = 24 when x = 2 and y = 3, find k.
• Combined Variation: If z varies directly as x and inversely as y, and z = 10 when x = 5 and y = 2, find k.