Final answer:
After setting up equations based on the information provided, we find that the number in question is 25, as four times 25 equals a century (100) and twice 25 equals a half-century (50).
Step-by-step explanation:
The question implies a mathematical problem involving algebraic expression and reasoning. To solve this, let's identify that 'a century' means 100 and 'a half-century' means 50. The question tells us 'four times this number is a century' and 'twice this number is a half-century', so we can set up two equations:
4x = 100 (century)
2x = 50 (half-century)
Both equations aim to find the same number, so we can use either one to get the answer. Using the second equation:
2x = 50
Divide both sides by 2 to isolate x:
x = 50 / 2
x = 25
Therefore, the number we are looking for is 25.