Chapter C, Problem 1PA

To determine

(a)

To calculate:

The percentage change from 8 to 12 using the mid-point method.

Answer to Problem 1PA

The percentage change from 8 to 12 is 80%.

Explanation of Solution

The midpoint formula computes percentage changes by dividing the change by the average value.

Percentage change is calculated as follows:

    $\begin{array}{l}Percentagechange=\frac{Q_2-Q_1}{AverageofQ}\times 100\\ Percentagechange=\frac{Q_2-Q_1}{(\frac{Q_2+Q_1}{2})}\times 100\\ Percentagechange=\frac{12-8}{(\frac{12+8}{2})}\times 100\\ Percentagechange=\frac{4}{\frac{20}{2}}\times 100\\ Percentagechange=\frac{4}{5}\times 100\\ Percentagechange=80\%\end{array}$

To determine

(b)

To calculate:

The percentage change in 18 to 14 using the mid-point method.

Answer to Problem 1PA

Quantity is decreased by '25%'.

Explanation of Solution

Percentage change can be calculated as follows:

  $\begin{array}{l}Percentagechange=\frac{Q_2-Q_1}{AverageofQ}\times 100\\ Percentagechange=\frac{Q_2-Q_1}{(\frac{Q_2+Q_1}{2})}\times 100\\ Percentagechange=\frac{14-18}{(\frac{14+18}{2})}\times 100\\ Percentagechange=-\frac{4}{\frac{32}{2}}\times 100\\ Percentagechange=-\frac{4}{16}\times 100\\ Percentagechange=-25\%\end{array}$

To determine

(c)

To calculate:

The percentage change in 130 to 120 using the mid-point method.

Answer to Problem 1PA

Quantity is decreased by '8%'.

Explanation of Solution

Percentage change can be calculated as follows:

  $\begin{array}{l}Percentagechange=\frac{Q_2-Q_1}{AverageofQ}\times 100\\ Percentagechange=\frac{Q_2-Q_1}{(\frac{Q_2+Q_1}{2})}\times 100\\ Percentagechange=\frac{120-130}{(\frac{120+130}{2})}\times 100\\ Percentagechange=-\frac{10}{\frac{250}{2}}\times 100\\ Percentagechange=-\frac{10}{125}\times 100\\ Percentagechange=-8\%\end{array}$

To determine

(d)

To calculate:

The percentage change in 95 to 105 using the mid-point method.

Answer to Problem 1PA

Quantity is increased by 10%.

Explanation of Solution

Percentage change can be calculated as follows:

  $\begin{array}{l}Percentagechange=\frac{Q_2-Q_1}{AverageofQ}\times 100\\ Percentagechange=\frac{Q_2-Q_1}{(\frac{Q_2+Q_1}{2})}\times 100\\ Percentagechange=\frac{105-95}{(\frac{105+95}{2})}\times 100\\ Percentagechange=\frac{10}{\frac{200}{2}}\times 100\\ Percentagechange=\frac{10}{100}\times 100\\ Percentagechange=10\%\end{array}$