Chapter 1.5, Problem 46E

To determine

To show: $\text{Three different pair of integers, each of which has a sum of -24}\text{.}$

Answer to Problem 46E

  $\text{The three pair of integers, each of which has a sum of -24 are:}$

  $\text{{(-12),(-12)};{(-36),(+12)};{(-72),(+48)}}$

Explanation of Solution

Given information :

  $\text{Each pair of integers has a sum of -24}\text{.}$

For the give question,

  $\text{Consider the sub-multiples and multiples of 24,}$

For the first pair,

  $\text{consider 12 ,which is a sub-multiple of 24}\text{.}$

  $\text{so, (-12)+(-12) = -24}\text{.}$

As both the integers are negative, the sum is also negative.

For the second pair,

  $\text{Consider -36 and +12, 36 is a multiple of 12,}$

  $\text{so, (-36)+(+12) = -24}\text{.}$

  $\left|-36\right|>\left|12\right|,\text{so the sum has the same sign as 36}\text{.}$

For the third pair,

  $\text{Consider -72 and +48 ,which are multiples of 24}\text{.}$

  $\text{so, (-72)+(+48) = -24}\text{.}$

  $\left|-72\right|>\left|48\right|,\text{so the sum has the same sign as 72}\text{.}$

Hence,

The three pair of integers are:

  $\text{{(-12),(-12)};{(-36),(+12)};{(-72),(+48)}}$