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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You're on a roll — Swali la 15: 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. Step 1: Andika milinganyo miwili kulingana na taarifa iliyotolewa. Acha x iwe idadi ya sarafu za shilingi 5. Acha y iwe idadi ya sarafu za shilingi 10. Jumla ya sarafu ni 100: x + y = 100 (Mlinganyo 1) Jumla ya thamani ya sarafu ni shilingi 600: 5x + 10y = 600 (Mlinganyo 2) Step 2: Tatua milinganyo kwa kutumia njia ya kubadilisha (substitution method). Kutoka Mlinganyo 1, toa x: x = 100 - y Step 3: Badilisha x katika Mlinganyo 2: 5(100 - y) + 10y = 600 500 - 5y + 10y = 600 500 + 5y = 600 Step 4: Tatua kwa y: 5y = 600 - 500 5y = 100 y = (100)/(5)