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The cost of a pen and a book are in the ratio of 5:3 respectively. If a pen costs sh. 2000, What is the cost of a book? 2. The cost of book and rulers in the ratio of 5:1. What is the cost of a book if a ruler costs costs sh. 250

Mathematics

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1. Tatizo la Kwanza:

  1. Andika uwiano wa gharama ya kalamu na kitabu.

    Gharama ya kalamu : Gharama ya kitabu = $5 : 3$.
    Tunajua gharama ya kalamu ni sh 2000.

  2. Weka uwiano kama mlinganyo ili kupata gharama ya kitabu.

    Hebu CkC_k iwe gharama ya kalamu na CbC_b iwe gharama ya kitabu.

    CkCb=53\frac{C_k}{C_b} = \frac{5}{3}

    Badilisha gharama ya kalamu:

    2000Cb=53\frac{2000}{C_b} = \frac{5}{3}
  3. Tatua mlinganyo kwa CbC_b.

    5×Cb=2000×35 \times C_b = 2000 \times 3 5Cb=60005 C_b = 6000

    Gawanya pande zote mbili kwa 5:

    Cb=60005C_b = \frac{6000}{5} Cb=1200C_b = 1200

    Gharama ya kitabu ni sh 1200.

    Gharama ya kitabu ni sh 1200\boxed{\text{sh 1200}}.

    2. Tatizo la Pili:

  4. Andika uwiano wa gharama ya kitabu na rula.

    Gharama ya kitabu : Gharama ya rula = $8 : 1$.
    Tunajua gharama ya rula ni sh 250.

  5. Weka uwiano kama mlinganyo ili kupata gharama ya kitabu.

    Hebu CbC_b iwe gharama ya kitabu na CrC_r iwe gharama ya rula.

    CbCr=81\frac{C_b}{C_r} = \frac{8}{1}

    Badilisha gharama ya rula:

    Cb250=81\frac{C_b}{250} = \frac{8}{1}
  6. Tatua mlinganyo kwa CbC_b.

    Cb×1=8×250C_b \times 1 = 8 \times 250 Cb=2000C_b = 2000

    Gharama ya kitabu ni sh 2000.

    Gharama ya kitabu ni sh 2000\boxed{\text{sh 2000}}.

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