Chapter 6.2, Problem 7E

To determine

To describe and correct the error in the given proportion for the cost of $30$ pencils.

Answer to Problem 7E

The error is found in left hand sideof the given proportion,the correct proportion is,

  $\frac{2}{12}=\frac{x}{30}$

The cost of $30$ pencils is $\$5$ .

Explanation of Solution

Given information:

The cost of the pencil is given as $\$2$ for per $12$ pencils.

The proportion for cost of $30$ pencils is given as,

  $\frac{12}{2}=\frac{x}{30}$

From the given data, the proportion for cost of $30$ pencils can be derived as,

  $\frac{2}{12}=\frac{x}{30}$

From comparing the given proportion $\frac{12}{2}=\frac{x}{30}$ with the derived proportion $\frac{2}{12}=\frac{x}{30}$ , the error is found as, $\frac{12}{2}$ that should be written as $\frac{2}{12}$ in the given proportion.

The cost of $30$ pencils can be calculated as,

  $\begin{array}{l}\frac{2}{12}=\frac{x}{30}\\ \frac{2}{12}\times 30=\frac{x}{30}\times 30\left[\text{multiply each side with 30}\right]\\ x=\frac{60}{12}\text{}\left[\text{divide}\right]\\ x=5\end{array}$

Therefore,

The cost of $30$ pencils is $\$5$ .