Solve each problem. If m varies jointly as x and y, and m=10 when x=2 and y=14, find m when x=21 and y=8.

Key Concepts

Joint Variation

Joint variation occurs when a variable is directly proportional to the product of two or more other variables. In this case, if m varies jointly as x and y, it can be expressed as m = kxy, where k is a constant of variation. Understanding this relationship is crucial for solving problems involving joint variation.

Finding the Constant of Variation

To solve for the constant of variation (k), you can use known values of the variables. In the given problem, you substitute m, x, and y into the joint variation equation to find k. This step is essential as it allows you to establish the relationship between the variables before solving for m with new values.

Substitution in Equations

Substitution involves replacing variables in an equation with known values to find unknowns. After determining the constant k, you substitute the new values of x and y into the joint variation equation to calculate m. This technique is fundamental in algebra for solving equations and finding specific values.