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Home » So, number of favorable selections: - Groen Casting

So, number of favorable selections: - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Summer weekly: 2.4 × 5 = <<2.4*5=12>>12 miles.

📌 Difference per week: 12 – 4 = <<12-4=8>>8 miles.

📌 Over 4 weeks: 8 × 4 = <<8*4=32>>32 miles.

📌 Two trained researchers analyzed dietary data over several months. Dr. Lee analyzed 140 records, Dr. Kim analyzed 75% more than Dr. Lee, and Dr. Patel analyzed 20% fewer than Dr. Kim. What is the total number of records analyzed?

📌 Dr. Kim: 140 + (0.75 × 140) = 140 + 105 = <<140+105=245>>245.

📌 Dr. Patel: 245 – (0.20 × 245) = 245 × 0.8 = <<245*0.8=196>>196.

📌 Total = 140 + 245 + 196 = <<140+245+196=581>>581.

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Now include the third congruence: \( k \equiv 2 \pmod{9} \)
Let \( k = 35b + 18 \). Then:
35b + 18 \equiv 2 \pmod{9}
Reduce modulo 9: \( 35 \equiv 8 \mod 9 \), \( 18 \equiv 0 \mod 9 \), s...
8b \equiv 2 \pmod{9}
Multiply both sides by the inverse of 8 modulo 9. Since \( 8 \cdot 8 =...
b \equiv 8 \cdot 2 = 16 \equiv 7 \pmod{9} \implies b = 9c + 7
k = 35(9c + 7) + 18 = 315c + 245 + 18 = 315c + 263
Thus, the smallest positive solution is when \( c = 0 \): \( k = 263 \...
The smallest such \( k \) is \( oxed{263} \).

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