Problem 54 - College Algebra

Question

Explain what is meant by joint variation. Give an example with your explanation.

Step-by-Step Solution

Answer

Joint variation refers to a situation where a quantity varies directly with the product of two or more other quantities. An example is when the production cost of an item varies directly with the quantity of materials used and the labor hours required.

Step 1: Defining Joint Variation

Joint variation (or combined variation) is the combination of direct and inverse variation. It occurs when a given quantity varies directly with the product of two (or more) other quantities or inversely with these quantities.

Step 2: Example of Joint Variation

Here is an example: The cost to produce a product (C) varies directly as the amount of materials (M) used and the number of labor hours (L) required. This can be expressed mathematically as \( C=k * (M * L) \) where 'k' is the constant of variation.

Step 3: Explanation of the Example

In this example, if the amount of materials or the number of labor hours increases or decreases, this will have a direct impact on the cost to produce the product. Furthermore, if both the amount of materials and labor hours increase or decrease, the cost will increase or decrease accordingly.