Problem 99 - Intermediate Algebra

Question

Dietitians often calculate a patient’s BMI (Body Mass Index) to screen for weight categories that may lead to health problems. BMI is a number that is calculated from one’s weight and height. It is an indication of a person’s total body weight that comes from fat. The formula for BMI, as it appears in dietary textbooks, is: $$ \mathrm{BMI}=\frac{\text { weight }(\mathrm{lb}) \cdot 703}{\text { height }^{2}\left(\text { in } .^{2}\right)} $$ Solve the formula for weight. (IMAGE CANT COPY)

Step-by-Step Solution

Answer

Weight = \( \frac{\text{BMI} \cdot \text{height}^2}{703} \).

Step 1: Understand the given formula

The formula for BMI is given as \( \text{BMI} = \frac{\text{weight (lb)} \cdot 703}{\text{height}^2 (\text{in.}^2)} \). Our goal is to solve this formula for weight.

Step 2: Rearrange the formula

To solve for weight, we need to isolate weight on one side of the equation. Start by multiplying both sides of the equation by height squared to eliminate the fraction: \( \text{BMI} \cdot \text{height}^2 = \text{weight} \cdot 703 \).

Step 3: Solve for weight

Now divide both sides by 703 to solve for weight: \( \text{weight} = \frac{\text{BMI} \cdot \text{height}^2}{703} \). This isolates the weight on one side of the equation.

Key Concepts

BMI Calculation

The Body Mass Index (BMI) is a simple numeric measure to assess whether a person has a healthy body weight relative to their height. It acts as a screening tool rather than a diagnostic tool. To calculate BMI, we use a formula that involves a person's weight and height.Here's how the formula works:

• The weight of the person is measured in pounds (lb).
• The height is measured in inches (in).

The BMI formula is: \[\text{BMI} = \frac{\text{weight (lb)} \cdot 703}{\text{height}^2 (\text{in.}^2)}\]This formula gives us a numerical value. Based on this value, we can categorize the BMI as underweight, normal weight, overweight, or obese, using standard BMI categories.Understanding BMI can be a useful first step. It allows individuals to evaluate if their weight falls into a healthy range.

Formula Manipulation

Formula manipulation involves rearranging an equation to isolate a specific variable. This requires basic algebraic operations like addition, subtraction, multiplication, and division. It might sound complicated at first, but with practice, it becomes intuitive.Let's take the BMI formula as an example. We are given:\[\text{BMI} = \frac{\text{weight (lb)} \cdot 703}{\text{height}^2 (\text{in.}^2)}\]Our task is to solve this equation for 'weight.' To do this, we need to rearrange the terms so that 'weight' stands alone on one side. The manipulation steps are as follows:

• First, multiply both sides by \(\text{height}^2\) to get rid of the denominator: \[\text{BMI} \cdot \text{height}^2 = \text{weight} \cdot 703\]
• Next, divide both sides by 703 to solve for 'weight': \[\text{weight} = \frac{\text{BMI} \cdot \text{height}^2}{703}\]

These steps illustrate how formula manipulation can effectively isolate a variable. Knowing how to manipulate formulas is an essential skill in algebra.

Solving for a Variable

Solving for a variable means isolating that variable on one side of an equation. This might involve several algebraic steps, including moving terms from one side to the other. In our BMI example, we solved for the 'weight' variable.To isolate a variable, here's a general approach:1. Identify the variable you need to solve for.2. Use inverse operations to move other elements away from the variable.3. Simplify the equation step-by-step.For our BMI example:

• We identified 'weight' as the variable to solve for.
• We eliminated the fraction by multiplying both sides by \(\text{height}^2\).
• We then divided by 703 to fully isolate 'weight'.

Breaking down the steps makes it easier to follow and understand the process. This method can be applied to any equation where you need to solve for a specific variable. Mastery of this technique is crucial in intermediate algebra and beyond.