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A student, Mariam, wants to wallpaper a wall measuring 3m by 2.4m. She has 4.7m² of wallpaper. If wallpaper is sold in rolls of 10m² costing shs. 32,000 per roll, how many rolls must she buy and how m

Mathematics

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8 steps

Hapa kuna suluhisho la Item 6:

Part a(i)· 2 steps

  1. Tafuta eneo la ukuta.

    Urefu wa ukuta = 300 cm=3 m300 \text{ cm} = 3 \text{ m}
    Upana wa ukuta = 240 cm=2.4 m240 \text{ cm} = 2.4 \text{ m}
    Eneo la ukuta = 3 m×2.4 m=7.2 m23 \text{ m} \times 2.4 \text{ m} = 7.2 \text{ m}^2

  2. Tafuta kiasi cha ziada cha karatasi ya ukuta kinachohitajika.

    Karatasi ya ukuta aliyonayo Mariam = 4.7 m24.7 \text{ m}^2
    Karatasi ya ukuta ya ziada inayohitajika = 7.2 m2−4.7 m2=2.5 m27.2 \text{ m}^2 - 4.7 \text{ m}^2 = 2.5 \text{ m}^2
    Mariam anahitaji kununua 2.5 m² zaidi ya karatasi ya ukuta.

Part a(ii)· 2 steps

  1. Tafuta idadi ya roli za karatasi ya ukuta anazopaswa kununua.

    Kila roli ina 10 m210 \text{ m}^2. Kwa kuwa anahitaji 2.5 m22.5 \text{ m}^2 na roli zinauzwa nzima, atalazimika kununua roli moja.
    Idadi ya roli za kununua = 1 roli.

  2. Tafuta gharama ya karatasi ya ukuta ya ziada.

    Gharama ya roli moja = shs. 32,000
    Gharama ya roli 1 = 1×32,000=shs. 32,0001 \times 32,000 = \text{shs. } 32,000
    Mariam atalipa shs. 32,000 kwa karatasi ya ukuta ya ziada.

Part b(i)· 3 steps

  1. Tafuta mapato yanayotozwa kodi kwa mfanyakazi mmoja.

    Mshahara ghafi kwa mfanyakazi = shs. 350,000
    Posho ya usafiri isiyotozwa kodi = shs. 90,000
    Mapato yanayotozwa kodi = 350,000−90,000=shs. 260,000350,000 - 90,000 = \text{shs. } 260,000

  2. Tafuta kodi ya mapato kwa mfanyakazi mmoja.

    • Bendi ya kwanza (0 - 100,000): Kiasi = shs. 100,000 Kiwango cha kodi = 0% Kodi = 100,000×0%=shs. 0100,000 \times 0\% = \text{shs. } 0

    • Bendi ya pili (100,001 - 200,000): Kiasi = 200,000−100,000=shs. 100,000200,000 - 100,000 = \text{shs. } 100,000 Kiwango cha kodi = 5% Kodi = 100,000×0.05=shs. 5,000100,000 \times 0.05 = \text{shs. } 5,000

    • Bendi ya tatu (200,001 - 300,000): Kiasi = 260,000−200,000=shs. 60,000260,000 - 200,000 = \text{shs. } 60,000 Kiwango cha kodi = 15% Kodi = 60,000×0.15=shs. 9,00060,000 \times 0.15 = \text{shs. } 9,000

    Jumla ya kodi ya mapato kwa mfanyakazi mmoja = 0+5,000+9,000=shs. 14,0000 + 5,000 + 9,000 = \text{shs. } 14,000

  3. Tafuta jumla ya kodi ya mapato Mariam atakayokata kutoka kwa wafanyakazi wake wote.

    Idadi ya wafanyakazi = 3
    Jumla ya kodi ya mapato = 14,000×3=shs. 42,00014,000 \times 3 = \text{shs. } 42,000
    Jumla ya kodi ya mapato Mariam atakayokata ni shs. 42,000.

Part b(ii)· 1 step

  1. Tafuta mshahara halisi (net salary) kwa kila mfanyakazi.

    Mshahara halisi = Mshahara ghafi - Kodi ya mapato kwa mfanyakazi
    Mshahara halisi = 350,000−14,000=shs. 336,000350,000 - 14,000 = \text{shs. } 336,000
    Mariam atamlipa kila mfanyakazi shs. 336,000 kama mshahara halisi.

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