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Wasomi, Nifafanulieni Hii Hesabu iliyotumiwa Hapa.

Discussion in 'Jukwaa la Elimu (Education Forum)' started by X-PASTER, Sep 14, 2012.

  1. X-PASTER

    X-PASTER Moderator

    #1
    Sep 14, 2012
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    Watu watatu (3), walinunua mikate, mmoja alinunua mikate mitano (5) na mwinginee mitatu (3) jumla wakawa na mikate minane (8), na mwenzao wa tatu yeye hakununua chochote...!


    Wote watatu, wakala kwa vipimo sawa, hakuna aliyezidisha wala kupunguza, kisha yule wa tatu akatoa shiling elfu nane (8,000), akawagawia wale wenzake wawili wagawane.


    Ugomvi ukawa katika kugawana zile pesa. Yule aliyenunua mikate mitano (5) akataka kuchuwa shilingi elfu tano (5,000), na shilingi elfu tatu (3,000) ampatie mwenzake. Yule mwenzake akataka wagawane sawa kwa sawa, yaani kila mmoja achukuwe shilingi elfu nne (4,000).


    Wakashtakia kwa hakimu... Maamuzi ya hakimu yakawa hivi:


    Aliye nunua mikate mitano (5) achukuwe shilingi efu saba (7,000) na aliyenunua mikate mitatu (3) achukuwe shilingi elfu moja (1,000).


    Aliyenunua mikate mitatu (3), alipo fahamishwa akakubali na kuridhika. Je hakimu alitumia fomula gani katika kugawa haki?


    fafanua...
     
  2. Shark

    Shark JF-Expert Member

    #2
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    Imegoma X-p,
    But wasiwasi wangu ni kwa huyo hakimu, TAKUKURU waingilie kati!!
     
  3. X-PASTER

    X-PASTER Moderator

    #3
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    Chemsha bongo mkuu, mahesabu tu hapo...!
     
  4. Prof Gamba

    Prof Gamba JF-Expert Member

    #4
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    Hakimu alikuwa sahihi, alitumia formula kulipwa kutokana na kiasi cha mkate alichotoa, hesabu za sehemu na asilimia, kwa harakaharaka ni kwamba kwa mikate 8 kila mmoja alikula mikate 2 na 2/3 ambayo ni 8/3. Kwa hiyo mchango wa mwenye mikate 3 kwa aliyetoa hela ilikuwa ni 1/3 ya mkate tuu. Wakati yule wa mitano ilikuwa ni mikate 2 na 1/3 ya mkate kwa aliyetoa hela.

    Kwenye mgawanyo wa pesa sasa, inabidi wachukue kwa asilimia ya mikate waliyochangia kumlisha ambaye hakuwa na mkate. Kwanza inabidi kujua kuwa kwenye hiyo 8000 kila mkate aliokula angekuwa ananunua kwa sh ngapi? Ambayo inakuwa ni 3000 kwa mkate mmoja (8/3y =8000 ~ y = 8000x3/8 = 3000. NB: Y = Bei ya mkate). Kwa hiyo aliyemchangia mkate wa 2 na 1/3 itakuwa ni sawa na 7/3 x3000 ambayo inakuwa ni thamani ya sh. 7000 na aliyechangia kiasi cha mkate 1/3 itakuwa 1/3 x3000, ambayo itakuwa ni thamani ya sh. 1000.

    Big up sana kwa hakimu ambaye anaziweza na hesabu na alikuwa sahihi kabisa.
     
  5. wijei

    wijei JF-Expert Member

    #5
    Sep 14, 2012
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    safi kabisa,nadhaani umepitia mathematics departiment udsm.
     
  6. X-PASTER

    X-PASTER Moderator

    #6
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    Unaonyesha kuwa unajuwa unacho kifanya, ila kuna njia rahisi zaidi... But sina budi kukupongeza kwa uelewa wako, wacha tusubiri wasomi wengine watasema nini.
     
  7. jamiif

    jamiif JF-Expert Member

    #7
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    anajuana na hakim ndio mana kampendelea!
     
  8. Autorun

    Autorun JF-Expert Member

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    yah! Safi sana mkuu upo sahihi kabisa ingawa uwezo wako niwa BAM
     
  9. Prof Gamba

    Prof Gamba JF-Expert Member

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    Wee! Jiheshimu mkuu. Mie nimesoma pure kabisa, tena Udsm. Nimegombana na akina Dr. Kakiko na Homomophirsm na ma abelian group, japo kwa sasa nasikia wamepewa akina Mwanzalima hizo functional analysis na abstruct algebra. Na MT100 za akina Dr Rugeiyam, utata mtupu. Hicho kitu hakiwezi kunishinda hata kidogo.
     
  10. Prof Gamba

    Prof Gamba JF-Expert Member

    #10
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    Ha ha ha ha!!! kwanza mkuu ilikuwa ni usiku, na wakati huo usingizi ulikuwa umeniishia huku nimelala, nikaamua kuanza kuperuzi kwenye sim yangu JF, ndo nikakutana na huu uzi. Kiujumla ningekuwa kwenye pc nadhani ningetumia approach nyingine. Lakini hesabu nimezisoma mpaka level ya chuo mkuu, kwa hiyo ni wajibu wangu, wala sio lazima pongezi, labda angekuwa ngwini.
     
  11. Prof Gamba

    Prof Gamba JF-Expert Member

    #11
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    Uko sahihi mkuu, nimepitia lile jengo lililo jirani na UCC kwenye kituo cha utawala UDSM.
     
  12. X-PASTER

    X-PASTER Moderator

    #12
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    <>Majibu<>


    1. Mikate: 8, ukigawa kila mkate vipande vitatu sawa 1/3 jumla vipande vitakuwa 24.
    2. Wamekula sawa kwa sawa, ina maana kila mmoja kala vipande 8. 1=8 x 3 = 24
    3. Yule wa mikate mitano (5) atatoa vipande 15 = (3 x 5 = 15) kwenye mikate yake, na amekulaa vipande 8 na kubakia vipande 7 = (15 - 8 = 7)
    4. Yule wa mikate mitano (3) atatoa vipande 9 = (3 x 3 = 9) kwenye mikate yake, na amekulaa vipande 8 na kubakia kipande 1 = (9 - 8 = 1)
    5. 7 ya kwanza jumlisha na 1 unapata vipande nane (8) alivyokula yule wa tatu.
    6. Kimahesabu, yule wa tatu kala Kipande kimoja (1) cha yule aliyetoa mikate 3 na kala vipande saba (7) kwa yule aliyetoa mikate 5... Kimalipo uwiano (ratio) ni 7:1
     
  13. e

    enoc Member

    #13
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    Haka niny tuachen kuumiza vchwa kwa ajir ya mambo ya kukariri, mana hyo hesabu hata cjaihelewa na hakim ambaye kasoma arts subjects anajua wap? Jama ukolon mambo leo ndo huu, kwasababu cc tunaishia kukariri v2 vya wanaume wenzentu na yna2fanya 2shindwe kufklia hata zaidi #haya maon 2 sasa 2ctukanane ila 2lijadil hlo.
     
  14. Narubongo

    Narubongo JF-Expert Member

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    kwa kutumia probabilistic approach
    assume wa 3 amelipa exact amount (8000/=) kwa alichokula. hakimu amegawa hela (8000/=) based on contribution of everyone to jamaa wa 3
    wa mikate 5 amecontribute 7000/8000 = 7/8 kumlisha wa 3
    wa mikate 3 amecontribute 1000/8000 = 1/8 kumlisha wa 3
    7/8+1/8 = 8/8 = 1

    ukitaka kujua kila mmoja alitoa vipande vingapi (X) kwa jamaa wa 3 fanya hivi

    7/8 * 8 = 7 (kwa jamaa wa kwanza)
    1/8 * 8 = 1 (kwa jamaa wa pili)
    --> kwahiyo jumla alikula vipande = 7+1 = 8 hence ni sawa kabisa na kusema kila mmoja alikula vipande 8!
    --> jumla vililiwa vipande 8 * 3 = 24

    note: swali halijasema kama mikate yote ililiwa na halijasema kila mkate ulikatwa vipande vingapi

    kudadadeki ng'ombe hazeeki maini
     
  15. salito

    salito JF-Expert Member

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    Una maakili kiongozi balaa
     
  16. Shark

    Shark JF-Expert Member

    #16
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    Hata wewe imekushinda?
    Kwenye haya madude ukiwepo wewe, NingaR na Fotunho sina wasiwasi.
     
  17. Narubongo

    Narubongo JF-Expert Member

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    Prof Gamba majibu yako hayajatulia X-PASTER mjibu yako ni sahihi japo step #1 hukuonesha ni jinsi gani umepata hivyo vipande 24, swali ni zuri na linasolvika kiuraisi kwa probabilistic maths without forcing some steps
     
    Last edited by a moderator: Jan 4, 2016
  18. M

    Mzawa Halisi JF-Expert Member

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    Njia fupi:

    watu watatu waligawana sawasawa, hivyo kila mmoja alikula 1/3
    Ambaye hakununua alilipa shilling 8,000 ambayo ni sawa na 1/3 ya gharama ya mikate yote.
    Hivyo thamani ya mikate yote ni 8,000 * watu 3 = 24,000
    Kwa vile mikate ilikuwa nane, basi mkate mmoja ni shilling 3,000
    Yule aliyenunua mikate mitatu alitoa shillingi 9,000 na wa mikate mitano alitoa 15,000.
    Ili kila mmoja kuchangia sawa, aliyetoa 9,000 atarudishiwa 1,000 na yule wa 15,000 atarudishiwa elfu saba na kufanya wote kuwa wametoa 8,000.
     
  19. X-PASTER

    X-PASTER Moderator

    #19
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    Ndio maana likawa swali, si mpaka kumegewa, kutafuniwa na kulishwa... Ila Hongereni nyote mliojaribu, waliosoma na kujaribu kimoyomoyo, na wale waliotaka kuandika kisha hawakupost kwa kuchelea kukosea...!

    Na hongera nyingi kwa kila aliyejibu swali ili.
     
  20. njiwa

    njiwa JF-Expert Member

    #20
    Sep 15, 2012
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    respect! nimekubali hii
     
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