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Home » Let the integers be \( x \) and \( x+1 \). - 500apps

Let the integers be \( x \) and \( x+1 \). - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 \( 8.5 / 1.25 = 6.8 \), but since parts are discrete, use exact value. However, previous examples use exact math. So:

📌 \( 8.5 \div 1.25 = 6.8 \). But let’s re-express:

📌 Actually, correct model: utilization = processing time / detection interval = 8.5 / 1.25 = 6.8 parts.

📌 But since question likely expects exact calculation:

📌 \( \frac{8.5}{1.25} = 6.8 \). However, in real systems, it’s approximate. But math olympiad may accept decimal.

📌 Time between part arrivals: \( \Delta t = 1.25 \) s.

📌 Processing time: \( T = 8.5 \) s.

📌 Number of parts in process at once: \( \frac{T}{\Delta t} = \frac{8.5}{1.25} = 6.8 \).

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Multiply both sides by 60:
+ x = 39.6
Since number of users must be integer, \( 39.6 \) suggests rounding —...
\times 60 = 39.6
This implies the model allows non-integer arithmetic, but \( x \) must...
\frac{32 + x}{60} = \frac{66}{100} = \frac{33}{50}
\Rightarrow 32 + x = 60 \times \frac{33}{50} = \frac{1980}{50} = 39.6
But since number of users is integer, \( 32 + x \) must be integer, so...
+ x = \frac{33}{50} \times 60 = 39.6
Contradiction. Instead, assume reported rate is approximate, but in ma...

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