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.
ScanSolve AI Answer
Haya hapa swali la umri ili ujifunze: Swali: Umri wa mtoto ni theluthi moja ya umri wa mama yake wa sasa. Miaka 5 ijayo, umri wa mtoto utakuwa nusu ya umri wa mama yake wa wakati huo. Tafuta umri wa mama wa sasa. Suluhisho: Step 1: Wacha M iwe umri wa mama wa sasa na T iwe umri wa mtoto wa sasa. Kutokana na taarifa ya kwanza: T = (1)/(3)M (Mlinganyo 1) Step 2: Miaka 5 ijayo: Umri wa mama utakuwa M+5. Umri wa mtoto utakuwa T+5. Kutokana na taarifa ya pili: T+5 = (1)/(2)(M+5) (Mlinganyo 2) Step 3: Badilisha T kutoka Mlinganyo 1 kwenda Mlinganyo 2. (1)/(3)M + 5 = (1)/(2)(M+5) Step 4: Panua upande wa kulia wa mlinganyo. (1)/(3)M + 5 = (1)/(2)M + (1)/(2) × 5 (1)/(3)M + 5 = (1)/(2)M + (5)/(2) Step 5: Kusanya vigezo vya M upande mmoja na namba upande mwingine. Toa (1)/(3)M kutoka pande zote mbili na toa (5)/(2) kutoka pande zote mbili. 5 - (5)/(2) = (1)/(2)M - (1)/(3)M Pata kigawo cha kawaida kwa namba (2) na kwa vigezo (6). (10)/(2) - (5)/(2) = (3)/(6)M - (2)/(6)M (5)/(2) = (1)/(6)M Step 6: Tatua kwa M kwa kuzidisha pande zote mbili kwa 6. M = (5)/(2) × 6 M = 5 × 3 M = 15 Jibu: Umri wa mama wa sasa ni miaka 15. Last free one today — make it count tomorrow, or type /upgrade for unlimited.