Problem 7 · Hikers with glasses
Turning $0.24$ into a reduced fraction: $\tfrac{6}{25}$.
Integer answer, at most 4 digitsIn a group of hikers, dividing the number of people wearing glasses by the number of people not wearing them gives exactly $0.24$. What is the minimum number of people in the group?
Copa Cangur · SCM
Medium
Closed answer
Reasoned solution
Key idea: the integer ratio $\tfrac{u}{s} = 0.24$ forces $u$ and $s$ to be multiples of one minimal pair.
$$0.24 = \frac{24}{100} = \frac{6}{25}.$$
Since $\tfrac{6}{25}$ is in lowest terms, we need $u = 6k$ and $s = 25k$ with $k \ge 1$. The smallest group comes from $k = 1$:
$$6 + 25 = 31\ \text{people}.$$
Answer: 31