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
Hapa kuna suluhisho: Step 1: Fafanua vigezo na uandike milinganyo ya gharama na mapato. Bei ya kununua yai moja = sh. 300 Bei ya kuuza yai moja = sh. 500 Jumla ya faida = sh. 3500 Acha N_s iwe idadi ya mayai yaliyouzwa. Acha X iwe idadi ya mayai yaliyovunjika. Acha N_b iwe idadi ya mayai yaliyonunuliwa. Jumla ya gharama (Total Cost, CP) = N_b × 300 Jumla ya mapato (Total Revenue, SP) = N_s × 500 Tunajua kuwa idadi ya mayai yaliyonunuliwa ni sawa na idadi ya mayai yaliyouzwa pamoja na yaliyovunjika: N_b = N_s + X Step 2: Tumia fomula ya faida na ubadilishe vigezo. Faida = Jumla ya Mapato - Jumla ya Gharama 3500 = (N_s × 500) - (N_b × 300) Badilisha N_b = N_s + X kwenye mlinganyo wa faida: 3500 = 500 N_s - 300 (N_s + X) 3500 = 500 N_s - 300 N_s - 300 X Step 3: Rahisisha mlinganyo. 3500 = 200 N_s - 300 X Gawanya mlinganyo mzima kwa 100 ili kurahisisha zaidi: 35 = 2 N_s - 3 X Step 4: Tatua kwa N_s na tambua masharti. Panga upya mlinganyo ili kupata N_s: 2 N_s = 35 + 3 X N_s = (35 + 3 X)/(2) Kwa kuwa N_s lazima iwe namba kamili (idadi ya mayai), 35 + 3X lazima iwe namba shufwa (even number). Kwa sababu 35 ni namba witiri (odd number), 3X lazima iwe namba witiri ili jumla yao iwe shufwa. Hii inamaanisha X lazima iwe namba witiri. Step 5: Chagua thamani ndogo zaidi ya X ambayo ni namba witiri na chanya. Katika matatizo kama haya ambapo thamani ya X haijatolewa, tunachukua thamani ndogo zaidi ya X inayowezekana ambayo inatoa jibu kamili. Chagua X = 1. Step 6: Kokotoa N_s kwa kutumia X=1. N_s = (35 + 3(1))/(2) N_s = (35 + 3)/(2) N_s = (38)/(2) N_s = 19 Step 7: Thibitisha jibu. Ikiwa N_s = 19 na X = 1: Idadi ya mayai yaliyonunuliwa N_b = N_s + X = 19 + 1 = 20. Jumla ya gharama = 20 × sh. 300 = sh. 6000. Jumla ya mapato = 19 × sh. 500 = sh. 9500. Faida = Jumla ya Mapato - Jumla ya Gharama = sh. 9500 - sh. 6000 = sh. 3500. Faida hii inalingana na faida iliyotolewa kwenye swali. Idadi ya mayai aliyouza ni: 19 That's 2 down. 3 left today — send the next one.