Chapter 7.6, Problem 1P

Last year, the population of South Skratchankle was 48,000. This year, the population is 60,000. By what percent did the population increase? Explain how to solve the problem two different ways.

To determine

To calculate: The increase in population increase.

Answer to Problem 1P

The population increases by $25\%$ .

Explanation of Solution

Given information:

The population of south Skratchanklewas $48000$ , and next year the population is $60000$ .

Calculation:

First way to obtain the percentage is to calculate what percent of $48000$ is $60000$ .

Use the below formula to obtain the percentage as,

  $\frac{a}{b}=\frac{c}{100}$ ..... (1)

Here, $a$ is $60000$ or new population, $b$ is $48000$ or old population and $c$ is the percentage to be calculated.

Substitute $60000$ for $a$ and $48000$ for $b$ in equation (1) to obtain the value of $c$ as,

  $\begin{array}{c}\frac{60000}{48000}=\frac{c}{100}\\ \frac{c}{100}=\frac{60}{48}\\ c=\frac{60\cdot 100}{48}\\ =125\end{array}$

Therefore, the percent $c$ is $125\%$ . So, the increase in percentage is calculated if $100\%$ is subtracted from the percent $c$ .

The increase in percentage is,

  $125-100=25\%$

Therefore, the increase in percentage is $25\%$ .

Second way is to calculate the change of increase, so the change of increase is obtained if original population is subtracted from new population.

So, the change of increase is calculated as,

  $\begin{array}{c}\frac{\text{change}}{\text{original}}=\frac{60000-48000}{48000}\\ =\frac{12000}{48000}\\ =\frac{1}{4}\end{array}$

The percentage of change is calculated as,

  $\frac{1}{4}\left(100\right)=25\%$

Therefore, the change in population increase is $25\%$ .

Conclusion:

Thus, the population increases by $25\%$ .