To determine the population of the town, given that [tex]\(\frac{3}{8}\)[/tex] of the town's population is 243 persons, follow these steps:
1. Understand the fraction given: The fraction [tex]\(\frac{3}{8}\)[/tex] represents part of the population. Specifically, [tex]\(\frac{3}{8}\)[/tex] of the total population equals 243 persons.
2. Set up the equation: Let [tex]\( P \)[/tex] represent the total population of the town. According to the problem, [tex]\(\frac{3}{8} \times P = 243\)[/tex].
3. Solve for the total population, [tex]\( P \)[/tex]:
[tex]\[
\frac{3}{8} \times P = 243
\][/tex]
4. Isolate [tex]\( P \)[/tex]: To find [tex]\( P \)[/tex], multiply both sides of the equation by the reciprocal of [tex]\(\frac{3}{8}\)[/tex], which is [tex]\(\frac{8}{3}\)[/tex]:
[tex]\[
P = 243 \times \frac{8}{3}
\][/tex]
5. Perform the multiplication:
[tex]\[
P = 243 \times \frac{8}{3} = 243 \times 2.\overline{6}
\][/tex]
Since [tex]\(243 \div 3 = 81\)[/tex], you then multiply [tex]\(81 \times 8\)[/tex]:
[tex]\[
P = 81 \times 8 = 648
\][/tex]
Therefore, the total population of the town is [tex]\(648\)[/tex] persons.
