Chapter 4.2, Problem 14P

To determine

To find: four consecutive odd integers such that the sum of the two greatest is four times the

smallest

Answer to Problem 14P

The required answer is: consecutive odd integers are 5, 7, 9 and 11

Explanation of Solution

Calculation:

Let the first odd integer be x

Let the second odd integer be x+2

Let the third odd integer be x+4

Let the fourth odd integer be x+6

  $(x+6)+(x+4)=4x$

(Sum of the two greatest is four times the smallest)

  $\begin{array}{l}2x+10=4x\\ 2x+10-2x=4x-2x\end{array}$

(Subtract 2 x from both sides)

  $\begin{array}{l}10=2x\\ \frac{10}{2}=\frac{2x}{2}\end{array}$

(Divide 2 on both sides)

  $5=x$

(Simplify)

First odd integer:

  $x=5$

Second odd integer:

  $\begin{array}{l}x+2=5+2\\ x+2=7\end{array}$

Third odd integer:

  $\begin{array}{l}x+4=5+4\\ x+4=9\end{array}$

Fourth odd integer:

  $\begin{array}{l}x+6=5+6\\ x+6=11\end{array}$

Therefore the consecutive odd integers are 5, 7, 9 and 11.