Chapter 8.1, Problem 44WE

To determine

To find: The greatest value of $c$ for the given equation and condition.

Answer to Problem 44WE

The greatest value of $c$ for $c<d$ is $7$ .

Explanation of Solution

Given:

The given equation is $5c+4d=79$ .

The given condition is $c<d$ .

Calculation:

Consider the given equation is,

  $5c+4d=79$

Then, the solution for $c$ is,

  $\begin{array}{l}5c+4d=79\\ c=\frac{79-4d}{5}\end{array}$

The table for the relation between $c$ and $d$ is shown in Table 1

Table 1

$d$	$c=\frac{79-4d}{5}$
3	$\begin{array}{c}c=\frac{79-4\left(3\right)}{5}\\ =\frac{67}{5}\end{array}$
4	$\begin{array}{c}c=\frac{79-4\left(4\right)}{5}\\ =\frac{63}{5}\end{array}$
5	$\begin{array}{c}c=\frac{79-4\left(5\right)}{5}\\ =\frac{59}{5}\end{array}$
6	$\begin{array}{c}c=\frac{79-4\left(6\right)}{5}\\ =11\end{array}$
7	$\begin{array}{c}c=\frac{79-4\left(7\right)}{5}\\ =\frac{51}{5}\end{array}$
8	$\begin{array}{c}c=\frac{79-4\left(8\right)}{5}\\ =\frac{47}{5}\end{array}$
9	$\begin{array}{c}c=\frac{79-4\left(9\right)}{5}\\ =\frac{43}{5}\end{array}$
10	$\begin{array}{c}c=\frac{79-4\left(10\right)}{5}\\ =\frac{39}{5}\end{array}$
11	$\begin{array}{c}c=\frac{79-4\left(11\right)}{5}\\ =\frac{35}{5}\\ =7\end{array}$
12	$\begin{array}{c}c=\frac{79-4\left(12\right)}{5}\\ =\frac{31}{5}\end{array}$

Thus, greatest value of $c$ for $c<d$ is $7$ .