## Related questions with answers

U.S. retail losses due to employee theft have increased from $\$ 15.9$ billion in $2008$ to $\$ 16.2$ billion in $2011$. Find the rate of change of retail losses due to employee theft.

Solution

VerifiedIf we denote $\textbf{the rate of change of retail losses}$ as $\textcolor{#c34632}{x}$ we obtain the following equation:

$\begin{align*} 15.9+x\%\cdot15.9&=16.2\\ x\%\cdot15.9&=16.2-15.9 \tag{\textcolor{#4257b2}{Using the addition principle.}}\\ x\%\cdot15.9&=0.3\\ \frac{x}{100}\cdot15.9&=0.3\\ \frac{x}{100}&=\frac{0.3}{15.9} \tag{\textcolor{#4257b2}{Using the multiplication principle.}}\\ x&=\frac{0.3\cdot100}{15.9}\\ x&=\frac{30}{15.9}\\ x&=\boxed{\textcolor{#c34632}{1.89}} \end{align*}$

The rate of change of retail losses due to employee theft is $\boxed{\textcolor{#c34632}{1.89\%}}$.

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