Problem 108 - Algebra and Trigonometry

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The reason that systems of linear inequalities are appropriate for modeling healthy weight is because guidelines give healthy weight ranges, rather than specific weights, for various heights.

Step-by-Step Solution

Answer

The statement makes sense. This is because the system of linear inequalities can perfectly model the healthy weight range for any given height unlike a system of linear equations which is more suited for fixed weights rather than ranges. Linear inequalities provide both lower and upper limit for healthy weight for every different height, thus creating a more appropriate model in this situation.

Step 1: Understand the concept

Systems of linear inequalities are best used when there are bounds or ranges to a solution. In this case, a healthy weight range rather than a specific weight is provided for various heights. It makes sense because the weights between these ranges are all considered healthy for each specific height.

Step 2: Application in this scenario

Upon examining the scenario, it's understood that there isn't a single value of 'healthy weight' for any height, but rather a range of values. If the healthy weight for a particular height is between a and b (where a < b), the inequality a <= weight <= b would represent the range, thus showing that systems of linear inequalities are suitable for this type of modeling.

Step 3: Validate the interpretation

Therefore, it would be reasonable to use a system of linear inequalities to model healthy weight ranges for various heights. This is due to the inherent nature of systems of linear inequalities that allow them to handle ranges, upper and lower restrictions of variables, which in this case are different weights based on individual heights.