Question

What’s is the amount of medicine required by a patient weight 174 pounds?

Answer 1

We are told that the amount of medicine (m) is proportional to the patient's body weight (w). Hence:

`m\text{ }\propto\text{ w}`

We can re-write this as:

`\begin{gathered} m\text{ = kw} \\ \text{where k is the constant of proportionality} \end{gathered}`

Given:

A patient weighing 116 pounds requires 126 milligrams.

Substituting the given data:

`\begin{gathered} 126\text{ = k }*\text{ 116} \\ k\text{ = }(126)/(116) \\ k\text{ = }(63)/(58) \end{gathered}`

The equation relating m and w is thus:

`m\text{ = }(63)/(58)w`

The amount of medicine for a patient weighing 174 pounds can be calculated by substitution:

`\begin{gathered} m\text{ = }(63)/(58)\text{ }*\text{ 174} \\ m\text{ = 189} \end{gathered}`

Hence, the amount of medicine is 189 milligrams