Problem 51 - College Algebra

Question

In your own words, explain how to solve a variation problem.

Step-by-Step Solution

Answer

Direct variation problems can be solved using the equation \(y = kx\), and inverse variation problems can be solved using the equation \(xy = k\). In both cases, solve for \(k\) first using provided values, and use that \(k\) to find the missing variable when given a value for the other.

Step 1: Understanding Direct Variation

In direct variation, as one variable increases, the other also increases and vice versa. This type of relationship can be expressed as \(y = kx\), where \(k\) represents the constant of variation.

Step 2: Solving Direct Variation Problems

To solve direct variation problems, one first needs to identify two things from the problem: the variables which are directly proportional to each other, and their corresponding values. These values are then substituted into the equation \(y = kx\). Solve for \(k\) and use that value to find the missing variable when given a value for the other.

Step 3: Understanding Inverse Variation

In an inverse variation, as one variable increases, the other decreases proportionately. This relationship can be expressed as \(xy = k\), where \(k\) represents the constant of variation.

Step 4: Solving Inverse Variation Problems

Similar to direct variation problems, to solve an inverse variation problem, identify the variables that vary inversely and their corresponding values. Substitute these values into the equation \(xy = k\). Solve for \(k\) and use that value to find the missing variable when given a value for the other.