This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Haya Sophia, twende na maswali haya. 3. Tatizo la Tatu: Step 1: Andika uwiano wa matooke yaliyopakiwa na wakulima. Mkulima wa kwanza : Mkulima wa pili = 2 : 5. Tunajua mkulima wa kwanza alipakia miganda 18. Step 2: Weka uwiano kama mlinganyo ili kupata idadi ya miganda aliyopakia mkulima wa pili. Hebu M_1 iwe miganda ya mkulima wa kwanza na M_2 iwe miganda ya mkulima wa pili. (M_1)/(M_2) = (2)/(5) Badilisha idadi ya miganda ya mkulima wa kwanza: (18)/(M_2) = (2)/(5) Step 3: Tatua mlinganyo kwa M_2. 2 × M_2 = 18 × 5 2 M_2 = 90 Gawanya pande zote mbili kwa 2: M_2 = (90)/(2) M_2 = 45 Mkulima wa pili alipakia miganda 45. Mkulima wa pili alipakia miganda 45. 4. Tatizo la Nne: Step 1: Andika uwiano wa watu wazima na watoto. Watu wazima : Watoto = 3 : 5. Tunajua kuna watoto 60. Step 2: Weka uwiano kama mlinganyo ili kupata idadi ya watu wazima. Hebu W iwe idadi ya watu wazima na T iwe idadi ya watoto. (W)/(T) = (3)/(5) Badilisha idadi ya watoto: (W)/(60) = (3)/(5) Step 3: Tatua mlinganyo kwa W. 5 × W = 3 × 60 5 W = 180 Gawanya pande zote mbili kwa 5: W = (180)/(5) W = 36 Kuna watu wazima 36. Kuna watu wazima 36. 5. Tatizo la Tano: Step 1: Andika uwiano wa miti mirefu na miti mifupi (pygmy). Miti mirefu : Miti mifupi = 2 : 3. Tunajua kuna miti mifupi 59. Step 2: Weka uwiano kama mlinganyo ili kupata idadi ya miti mirefu. Hebu M_m iwe idadi ya miti mirefu na M_f iwe idadi ya miti mifupi. (M_m)/(M_f) = (2)/(3) Badilisha idadi ya miti mifupi: (M_m)/(59) = (2)/(3) Step 3: Tatua mlinganyo kwa M_m. 3 × M_m = 2 × 59 3 M_m = 118 Gawanya pande zote mbili kwa 3: M_m = (118)/(3) M_m ≈ 39.33 Kwa kuwa idadi ya miti lazima iwe namba kamili, kunaweza kuwa na tatizo katika swali au tunapaswa kuzungusha. Tukizungusha hadi namba kamili iliyo karibu, tunapata 39. Kuna miti mirefu 39. 3 done, 2 left today. You're making progress.