Chapter 5, Problem 32CR

To determine

To find:The proportional relationship between the cost and number of books and the constant of proportionality.

Answer to Problem 32CR

The cost of the book is not proportional to the number of books and thus no constant of proportionality.

Explanation of Solution

Given information:

The different number of books to their cost is shown in the below table.

Books	$2$	$4$	$6$	$8$
Cost ($)	$2$	$5$	$7$	$10$

Calculation:

Two quantities in which the ratio or rate is constant, then they are to be said proportional and if the rates are not constant, then the quantities are said to be non-proportional. The constant ratio which is defining whether the two quantities are said to be proportional or not is known as constant of proportionality.

The expression for cost of $2$ books in ratio from the given table is:

  $\frac{\$2}{2}$

To obtain the rate of $\frac{\$2}{2}$ , divide the numerator and denominator of the above expression by $2$ .

  $\frac{\$2}{2}\frac{÷}{÷}\frac{2}{2}=\$1$

The expression for cost of $4$ books in ratio from the given table is:

  $\frac{\$5}{4}$

To obtain the rate of $\frac{\$5}{4}$ , divide the numerator and denominator of the above expression by $4$ .

  $\frac{\$5}{4}\frac{÷}{÷}\frac{4}{4}=\$1.25$

The expression for cost of $6$ books in ratio from the given table is:

  $\frac{\$7}{6}$

To obtain the rate of $\frac{\$7}{6}$ , divide the numerator and denominator of the above expression by $6$ .

  $\frac{\$7}{6}\frac{÷}{÷}\frac{6}{6}=\$1.167$

The expression for cost of $8$ books in ratio from the given table is:

  $\frac{\$10}{8}$

To obtain the rate of $\frac{\$10}{8}$ , divide the numerator and denominator of the above expression by $8$ .

  $\frac{\$10}{8}\frac{÷}{÷}\frac{8}{8}=\$1.25$

Since each rate of the above is not equal to each other thus there is no constant of proportionality.

Therefore, the cost of the books is proportional to the number of the books and thus no constant of proportionality.