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A teacher from a government school is saving for the years he has taught. He has 120 million on his account and wants to use his savings to construct single and double rooms for rentals.

Mathematics

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2 parts
a

Sh. 4,200,000\text{Sh. } 4,200,000

Sh. 2,700,000\text{Sh. } 2,700,000

Sh. 3,600,000\text{Sh. } 3,600,000

c

Ndio, tarehe hiyo inafaa.\text{Ndio, tarehe hiyo inafaa.}

Step-by-step solution

5 steps

ITEM 1

Part a· 3 steps

Kuhesabu kiasi ambacho kila mmoja atapokea

  1. Kokotoa sehemu yako (wewe, mkubwa).

    Wewe unapokea 40%40\% ya Sh. 10,500,000.

    Sehemu yako=0.40×10,500,000=Sh. 4,200,000\text{Sehemu yako} = 0.40 \times 10,500,000 = \text{Sh. } 4,200,000

  2. Kokotoa kiasi kilichobaki baada ya wewe kuchukua sehemu yako.

    Kiasi kilichobaki=10,500,000−4,200,000=Sh. 6,300,000\text{Kiasi kilichobaki} = 10,500,000 - 4,200,000 = \text{Sh. } 6,300,000

  3. Gawanya kiasi kilichobaki kati ya Moses na Joshua kwa uwiano wa $3:4$.

    Jumla ya sehemu za uwiano ni 3+4=73 + 4 = 7.
    Sehemu ya Moses:

    Sehemu ya Moses=37×6,300,000=3×900,000=Sh. 2,700,000\text{Sehemu ya Moses} = \frac{3}{7} \times 6,300,000 = 3 \times 900,000 = \text{Sh. } 2,700,000

    Sehemu ya Joshua:

    Sehemu ya Joshua=47×6,300,000=4×900,000=Sh. 3,600,000\text{Sehemu ya Joshua} = \frac{4}{7} \times 6,300,000 = 4 \times 900,000 = \text{Sh. } 3,600,000

    Kiasi ambacho kila mmoja atapokea ni:

    • Wewe: Sh. 4,200,000\boxed{\text{Sh. } 4,200,000}
    • Moses: Sh. 2,700,000\boxed{\text{Sh. } 2,700,000}
    • Joshua: Sh. 3,600,000\boxed{\text{Sh. } 3,600,000}

Part b· 2 steps

Kuamua tarehe inayofuata ambayo nyote watatu mtakutana benki

  1. Tafuta Kigawo Kidogo Zaidi cha Pamoja (LCM) cha idadi ya siku za ziara zenu.

    Wewe: kila siku 8
    Moses: kila siku 12
    Joshua: kila siku 15
    Kutafuta LCM ya 8, 12, na 15:
    8=238 = 2^3
    12=22×312 = 2^2 \times 3
    15=3×515 = 3 \times 5

    LCM(8,12,15)=23×3×5=8×3×5=120 siku\text{LCM}(8, 12, 15) = 2^3 \times 3 \times 5 = 8 \times 3 \times 5 = 120 \text{ siku}

    Mtakutana tena baada ya siku 120.

  2. Kokotoa tarehe inayofuata kuanzia tarehe ya mwisho ya kukutana (Mei 5).

    • Siku zilizobaki mwezi Mei (Mei 5 hadi Mei 31): 31−5=2631 - 5 = 26 siku.
    • Siku zilizobaki: 120−26=94120 - 26 = 94 siku.
    • Mwezi Juni: 30 siku. Siku zilizobaki: 94−30=6494 - 30 = 64 siku.
    • Mwezi Julai: 31 siku. Siku zilizobaki: 64−31=3364 - 31 = 33 siku.
    • Mwezi Agosti: 31 siku. Siku zilizobaki: 33−31=233 - 31 = 2 siku. Hii inamaanisha siku 2 za mwezi unaofuata. Tarehe inayofuata mtakayokutana ni Septemba 2.

Part c

Ndio, tarehe hiyo inafaa.\text{Ndio, tarehe hiyo inafaa.}

Kuamua kama tarehe hiyo inafaa kwa nyote watatu kumtembelea baba yenu

Tarehe ya kukutana ni Septemba 2.

  • Joshua ana safari Agosti 4. Tarehe hii ni kabla ya Septemba 2, kwa hivyo Joshua atakuwa amerudi na atapatikana.
  • Moses ana mtihani Septemba 6. Tarehe ya kukutana (Septemba 2) ni siku nne kabla ya mtihani wake. Ingawa ni karibu na mtihani, Moses bado atakuwa huru na anaweza kuhudhuria ziara hiyo.

Kwa hivyo, tarehe ya Septemba 2 inafaa kwa nyote watatu kumtembelea baba yenu.
Jibu: Ndio, tarehe hiyo inafaa.\boxed{\text{Ndio, tarehe hiyo inafaa.}}

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