One side of a parking stall is defined by a straight stripe that consists of n painted sections of equal length with an unpainted section 1/2 as long between each pair of consecutive painted sections

题目

One side of a parking stall is defined by a straight stripe that consists of n painted sections of equal length with an unpainted section 1/2 as long between each pair of consecutive painted sections. The total length of the stripe from the beginning of the first painted section to the end of the last painted section is 203 inches. If n is an integer and the length, in inches, of each unpainted section is an integer greater than 2, what is the value of n ?

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解析

涂色段长度 = \(x\) 未涂色段长度 = \(\frac{x}{2}\) 涂色段数量 = \(n\) 未涂色段数量 = \(n-1\) \[ n \cdot x + (n-1) \cdot \frac{x}{2} = 203 \] \[ \frac{x}{2}(3n - 1) = 203 \] \[ \frac{x}{2}(3n - 1) = 1 \times 203 = 7 \times 29 \] 由于\(x\)是大于2的整数，因此舍去\(1 \times 203\)的情况。 \(3n-1 = 7\) 或 \(29\) 若\(3n-1 = 7\) \(n = \frac{8}{3}\)（舍去）若\(3n-1 = 29\) \(n = 10\)

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