Chapter 13.5, Problem 38HP

To determine

To find: Sum of all possible values of $c$ .

Answer to Problem 38HP

Sum of values of $c$ is $21$

Explanation of Solution

Given information:

  $4c+d=26$

  $c,d$ are positive integers.

  $\begin{array}{l}4c+d=26\\ \Rightarrow 4c=26-d\\ \Rightarrow c=\frac{26-d}{4}\end{array}$

For $c$ to be integer

  $d=2,6,10,14,18,22$

Therefore,

Values of $c$ are

  $\begin{array}{l}c=\frac{26-2}{4}=\frac{24}{4}=6\\ c=\frac{26-6}{4}=\frac{20}{4}=5\\ c=\frac{26-10}{4}=\frac{16}{4}=4\\ c=\frac{26-14}{4}=\frac{12}{4}=3\\ c=\frac{26-18}{4}=\frac{8}{4}=2\\ c=\frac{26-22}{4}=\frac{4}{4}=1\\ \end{array}$

Therefore,

Values of $c$ are $1,2,3,4,5,6$

Sum of values of $c$ is $1+2+3+4+5+6=21$