Chapter 8.7, Problem 59IP

(a)

To determine

Write and solve inequality to find how much her temperature must increase before she is considered to have a high fever.

Answer to Problem 59IP

99.2 + x >101; more than ${1.8}^0 \text{F}$

Explanation of Solution

Given:

Suppose Malia has a temperature of $\text{99}{\text{.2}}^0 \text{F}$ . Write and solve inequality to find how much her temperature must increase before she is considered to have a high fever.

  

Concept Used:

Let x be the temperature need to increase.

The required inequality: $99.2+x>101$

Calculation:

The required inequality: $99.2+x>101$

  $\begin{array}{l}99.2+x>101 \\ 99.2-99.2+x>101-99.2 \text{[}\text{Subtract}99.2\text{from}\text{both}\text{sides}\text{]} \\ x>1.8\end{array}$

Thus, her temperature must increase more than ${1.8}^0 \text{F}$ before she is considered to have a high fever.

(b)

To determine

Write and solve an inequality that describes how much lower the body temperature of a person with hypothermia will be than the body temperature of a person with a normal temperature of 98.6 deg F.

Answer to Problem 59IP

  $95+x<98.6$

Explanation of Solution

Given:

  

Hypothermia occurs when a person`s body temperature falls below 95 deg F. Write and solve an inequality that describes how much lower the body temperature of a person with hypothermia will be than the body temperature of a person with a normal temperature of 98.6 deg F.

Concept Used:

Let x be the required temperature.

The required inequality $95+x<98.6$

Calculation:

The required inequality $95+x<98.6$

  $\begin{array}{l}95+x<98.6\\ 95-\text{95}+x<98.6-95 \text{[}\text{Subtract}95\text{from}\text{both}\text{sides}\text{]}\\ x<3.6\end{array}$

Thus, less than ${3.6}^0 \text{F}$ lower the body temperature of a person.