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
Step 1: Fafanua vigezo na uandike milinganyo. Acha b iwe gharama ya mkate mmoja na m iwe gharama ya pakiti moja ya maziwa. Kutokana na taarifa ya kwanza, tuna mlinganyo: 4b + 3m = 410 (Mlinganyo 1) Kutokana na taarifa ya pili, tuna mlinganyo: 3b + 2m = 290 (Mlinganyo 2) Step 2: Tumia njia ya kuondoa (elimination method) kutatua milinganyo. Ili kuondoa m, zidisha Mlinganyo 1 kwa 2 na Mlinganyo 2 kwa 3: Zidisha Mlinganyo 1 kwa 2: 2(4b + 3m) = 2(410) 8b + 6m = 820 (Mlinganyo 3) Zidisha Mlinganyo 2 kwa 3: 3(3b + 2m) = 3(290) 9b + 6m = 870 (Mlinganyo 4) Step 3: Toa Mlinganyo 3 kutoka Mlinganyo 4 ili kupata thamani ya b. (9b + 6m) - (8b + 6m) = 870 - 820 9b - 8b + 6m - 6m = 50 b = 50 Hivyo, gharama ya mkate mmoja ni Sh. 50. Step 4: Badilisha thamani ya b katika Mlinganyo 1 ili kupata thamani ya m. 4b + 3m = 410 4(50) + 3m = 410 200 + 3m = 410 3m = 410 - 200 3m = 210 m = (210)/(3) m = 70 Hivyo, gharama ya pakiti moja ya maziwa ni Sh. 70. Gharama ya mkate: Sh. 50, Gharama ya maziwa: Sh. 70 Got more? Send 'em.