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Help the youth group to determine: The actual area of the piece of the land in km2 The time the tractors shall plough the 10 acres Find the total budget for ploughing

Mathematics

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3 parts
a

25 km2\text{25 } km^2

b

2 masaa, 18 dakika na 28 sekunde\text{2 masaa, 18 dakika na 28 sekunde}

c

UGX 13,714,286\text{UGX 13,714,286}

Step-by-step solution

11 steps

Haya, twende tukasuluhishe swali hili hatua kwa hatua.

Part a· 2 steps

Eneo halisi la kipande cha ardhi katika km2km^2

  1. Badilisha kiwango cha ramani kutoka cmcm hadi kmkm.

    Kiwango cha ramani ni 1:250,0001:250,000, ambayo inamaanisha 1 cm1 \, cm kwenye ramani inawakilisha 250,000 cm250,000 \, cm ardhini.
    Tunajua kuwa 100 cm=1 m100 \, cm = 1 \, m na 1000 m=1 km1000 \, m = 1 \, km.
    Hivyo, 250,000 cm=250,000100 m=2,500 m250,000 \, cm = \frac{250,000}{100} \, m = 2,500 \, m.
    Na 2,500 m=2,5001000 km=2.5 km2,500 \, m = \frac{2,500}{1000} \, km = 2.5 \, km.
    Kwa hiyo, 1 cm1 \, cm kwenye ramani inawakilisha 2.5 km2.5 \, km ardhini.

  2. Kokotoa eneo halisi.

    Kwa eneo, tunapiga mraba kiwango cha urefu.
    1 cm21 \, cm^2 kwenye ramani inawakilisha (2.5 km)2(2.5 \, km)^2 ardhini.
    (2.5 km)2=6.25 km2(2.5 \, km)^2 = 6.25 \, km^2.
    Eneo kwenye ramani ni 4 cm24 \, cm^2.
    Eneo halisi = Eneo kwenye ramani ×\times (Kiwango cha eneo)
    Eneo halisi = 4 cm2×6.25 km2cm2=25 km24 \, cm^2 \times 6.25 \, \frac{km^2}{cm^2} = 25 \, km^2.

    Eneo halisi la kipande cha ardhi ni 25 km2\boxed{\text{25 } km^2}.

Part b

2 masaa, 18 dakika na 28 sekunde\text{2 masaa, 18 dakika na 28 sekunde}

Muda ambao matrekta yatatumia kulima ekari 10

  1. Tafuta kiwango cha kulima kwa kila trekta.

    Trekta A hulima ekari 1 kwa dakika 45. Kiwango cha A (RAR_A) = 1 ekari45 dakika\frac{1 \, \text{ekari}}{45 \, \text{dakika}}.
    Trekta B hulima ekari 1 kwa dakika 20. Kiwango cha B (RBR_B) = 1 ekari20 dakika\frac{1 \, \text{ekari}}{20 \, \text{dakika}}.

  2. Tafuta kiwango cha kulima cha matrekta yote mawili yakifanya kazi pamoja.

    Kiwango cha pamoja (RjumlaR_{jumla}) = RA+RBR_A + R_B

    Rjumla=145+120 ekari/dakikaR_{jumla} = \frac{1}{45} + \frac{1}{20} \, \text{ekari/dakika}

    Ili kujumlisha sehemu hizi, tunatafuta kigawo cha kawaida kidogo (LCM) cha 45 na 20, ambacho ni 180.

    Rjumla=1×445×4+1×920×9=4180+9180=13180 ekari/dakikaR_{jumla} = \frac{1 \times 4}{45 \times 4} + \frac{1 \times 9}{20 \times 9} = \frac{4}{180} + \frac{9}{180} = \frac{13}{180} \, \text{ekari/dakika}
  3. Kokotoa muda unaohitajika kulima ekari 10.

    Muda = Jumla ya ardhiKiwango cha pamoja\frac{\text{Jumla ya ardhi}}{\text{Kiwango cha pamoja}}

    Muda=10 ekari13180 ekari/dakika=10×18013 dakika=180013 dakikaMuda = \frac{10 \, \text{ekari}}{\frac{13}{180} \, \text{ekari/dakika}} = 10 \times \frac{180}{13} \, \text{dakika} = \frac{1800}{13} \, \text{dakika}
  4. Badilisha muda kuwa masaa na dakika.

    180013 dakika≈138.46 dakika\frac{1800}{13} \, \text{dakika} \approx 138.46 \, \text{dakika}

    138 dakika ni sawa na 2 masaa na 18 dakika (138=2×60+18138 = 2 \times 60 + 18).
    Sehemu iliyobaki ya dakika ni 0.46×60≈280.46 \times 60 \approx 28 sekunde.

    Muda ambao matrekta yatatumia kulima ekari 10 ni takriban 2 masaa, 18 dakika na 28 sekunde\boxed{\text{2 masaa, 18 dakika na 28 sekunde}}.

Part c

UGX 13,714,286\text{UGX 13,714,286}

Tafuta bajeti yote ya kulima

  1. Eleza michango kama sehemu ya bajeti yote.

    Acha bajeti yote iwe BB.
    Mchango wa Clergy = 25B\frac{2}{5} B.
    Mchango wa MP = 14B\frac{1}{4} B.

  2. Kokotoa sehemu ya bajeti iliyobaki baada ya michango ya Clergy na MP.

    Jumla ya michango ya Clergy na MP = 25B+14B=(820+520)B=1320B\frac{2}{5} B + \frac{1}{4} B = \left(\frac{8}{20} + \frac{5}{20}\right) B = \frac{13}{20} B.
    Sehemu iliyobaki = B−1320B=720BB - \frac{13}{20} B = \frac{7}{20} B.

  3. Kokotoa mchango wa wanachama wa kikundi.

    Wanachama wa kikundi huchangia nusu ya sehemu iliyobaki.
    Mchango wa wanachama wa kikundi = 12×720B=740B\frac{1}{2} \times \frac{7}{20} B = \frac{7}{40} B.

  4. Kokotoa jumla ya mchango wa wanachama wa kikundi kwa pesa.

    Kila mwanachama 1 kati ya 48 alichangia UGX 50,000.
    Jumla ya mchango wa wanachama wa kikundi = 48×50,000 UGX=2,400,000 UGX48 \times 50,000 \, \text{UGX} = 2,400,000 \, \text{UGX}.

  5. Linganisha mchango wa wanachama wa kikundi na sehemu yake ya bajeti ili kupata bajeti yote.

    740B=2,400,000 UGX\frac{7}{40} B = 2,400,000 \, \text{UGX} B=2,400,000×407 UGXB = 2,400,000 \times \frac{40}{7} \, \text{UGX} B=96,000,0007 UGXB = \frac{96,000,000}{7} \, \text{UGX} B≈13,714,285.71 UGXB \approx 13,714,285.71 \, \text{UGX}

    Tunazungusha hadi shilingi iliyo karibu zaidi.

    Bajeti yote ya kulima ni takriban UGX 13,714,286\boxed{\text{UGX 13,714,286}}.

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