Matematika Rekreasi

  1. Dua bilangan dua angka, dibaca dari kiri ke kanan nilainya lebih besar 4.5 kali dari bila dibaca dari kanan ke kiri. Bilangan berapakah itu?
    Misalkan bilangan dua angka 12, kalau dibaca dari kiri nilainya 12. Tetapi kalau dibaca dari kanan nilainya 21, apabila dibandingkan 12 dan 21 maka 21 = 7/4 x 12.
Jawab:
Misal bilangan tersebut dinotasikan ab. Maka bilangan tersebut bila dibaca dari kiri memiliki nilai
ab = 10.a + b
Tetapi bila dibaca dari kanan memiliki nilai
ba = 10.b + a.
Diketahui ab = 4.5 ba, dengan demikian
10.a + b = 4.5 x (10.b +a) <==> 10a + b = 45b +4.5a <==> (10 - 4.5) a = (45 - 1) b
atau
5.5 a = 44 b <==> 55 a = 440 b.
Selanjutnya dengan mendaftar nilai a diperoleh
  • Untuk a = 0, tidak mungkin karena akan diperoleh bilangan satu angka 00 = 0.
  • Untuk a = 1, juga tidak mungkin karena akan menghasilkan bilangan rasional untuk b.
  • Kasus yang sama untuk a = 2,3,4,5,6,7, dan 9, menghasilkan bilangan rasional untuk b.
  • Khusus untuk a = 8, akan menghasilkan bilangan bulat b = 1.
Dengan demikian bilangan yang dimaksud adalah 81.
Catatan:
Dengan penjelasan di atas, persoalan dapat dikembangkan sesuai keinginan. Baik untuk bilangan dua digit angka atau tiga digit. Ada yang mau mencoba!
(Sumber Blog Jurusan Matematika UM)
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