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Kassim ana sanduku la pesa lenye sarafu 100 zilizochanganywa za shilingi 5 na shilingi 10, zenye thamani ya jumla ya shilingi 600. Tafuta idadi ya kila aina ya sarafu zilizomo kwenye sanduku.

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Kassim ana sanduku la pesa lenye sarafu 100 zilizochanganywa za shilingi 5 na shilingi 10, zenye thamani ya jumla ya shilingi 600. Tafuta idadi ya kila aina ya sarafu zilizomo kwenye sanduku.

  1. Andika milinganyo miwili kulingana na taarifa iliyotolewa.

    Acha xx iwe idadi ya sarafu za shilingi 5.
    Acha yy iwe idadi ya sarafu za shilingi 10.

    Jumla ya sarafu ni 100:

    x+y=100(Mlinganyo 1)x + y = 100 \quad \text{(Mlinganyo 1)}

    Jumla ya thamani ya sarafu ni shilingi 600:

    5x+10y=600(Mlinganyo 2)5x + 10y = 600 \quad \text{(Mlinganyo 2)}

  2. Tatua milinganyo kwa kutumia njia ya kubadilisha (substitution method).

    Kutoka Mlinganyo 1, toa xx:

    x=100−yx = 100 - y

  3. Badilisha xx katika Mlinganyo 2

    5(100−y)+10y=6005(100 - y) + 10y = 600 500−5y+10y=600500 - 5y + 10y = 600 500+5y=600500 + 5y = 600

  4. Tatua kwa yy

    5y=600−5005y = 600 - 500 5y=1005y = 100 y=1005y = \frac{100}{5}
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