Find the percent of decrease if the original population was 800 and the new population is 716.

Solution

VerifiedGiven:

$\begin{align*} \text{Original number}=800 \\ \text{New number}=716 \end{align*}$

We note that the new value is lower than the original value and thus we have a decrease in the value.

We then first determine the amount of the decrease, which is obtained by subtracting the original value from the new value.

$\begin{align*} \text{Amount of decrease}&=\text{Original value}-\text{New number} \\ &=800-716 \\ &=84 \end{align*}$

Next, we obtain the percent of decrease by dividing the amount of decrease by the original value and multiply the results by 100.

$\begin{align*} \text{Percent of decrease}&=\frac{\text{Amount of decrease}}{\text{Original number}}\cdot 100 \\ &=\frac{84}{800}\cdot 100 \\ &=\frac{21}{200}\cdot 100 \\ &=0.105\cdot 100 \\ &=10.5 \end{align*}$

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