A person's body mass index (BMI) is a function of their weight W (in kg ) and height H (in m ) g

step 1 In this problem, we will cover working backwards with a two -variable function. So we are given

A person's body mass index (BMI) is a function of their...

A person's body mass index (BMI) is a function of their weight $W$ (in $\mathrm{kg}$ ) and height $H$ (in $\mathrm{m}$ ) given by $B(W, H)=W / H^{2}$. With a BMI less than $18.5,$ a person is considered underweight. What is the possible range of weights for an underweight person $1.58 \mathrm{m}$ tall?

A person's body mass index (BMI) is a function of their weight $W$ (in $\mathrm{kg}$ ) and height $H$ (in $\mathrm{m}$ ) given by $B(W, H)=W / H^{2}$.
With a BMI less than $18.5,$ a person is considered underweight. What is the possible range of weights for an underweight person $1.58 \mathrm{m}$ tall?

Key Concepts

Body Mass Index (BMI)

BMI is a numerical measure derived from an individual's weight and height that is used as a general indicator of whether a person has a healthy body weight for a given height. It is calculated by dividing the weight in kilograms by the square of the height in meters. Understanding BMI is important for categorizing underweight, normal weight, overweight, and obesity ranges with respect to health risks.

Function Evaluation

Function evaluation involves substituting specific numerical values into a given formula or function. In the context of BMI, when provided with a particular height, the height value is substituted into the formula to transform it into an expression solely in terms of weight. This process simplifies the inequality and helps in identifying the range of weight values that meet certain health criteria.

Inequality Solving

Inequality solving is a critical mathematical skill where one finds the set of all possible values of a variable that satisfy a given inequality. In this case, after substituting the height value into the BMI formula, solving the inequality for weight involves isolating the weight variable on one side, leading to the determination of the upper limit for a BMI corresponding to the underweight category.

Algebraic Manipulation

Algebraic manipulation refers to the techniques used to rearrange and simplify equations or inequalities. This process includes substitution, multiplication, division, and the proper handling of expressions in order to isolate the variable of interest. It is essential in converting the BMI formula into a form that clearly shows the range of weight values that yield a BMI below the specified threshold.

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