A number of nurses working in Nairobi referral hospital decided to raise Kshs 144000 to buy a plot of land in Kenya in order to put their private health clinic. Each nurse was to contribute the same amount. But unfortunately before the contribution we're collected,five of the nurses retired. This meant that the remaining contributors had to pay more money to meet the target and each nurses had to add Kshs 2400 on contribution to bridge the gap of those who retired. TASK Find the number of nurses originally at Nairobi referral hospital and how would each nurse have contributed to the nearest shilling if 5 nurses had not retired.

Hebu tutatue tatizo hili: a) Tafuta idadi ya wauguzi waliokuwepo awali katika hospitali ya rufaa ya Nairobi. b) Tafuta kiasi ambacho kila muuguzi angechangia, kwa shilingi iliyo karibu, kama wauguzi 5 wasingestaafu. Hatua ya 1: Fafanua vigezo na uandike milinganyo ya awali. Acha N iwe idadi ya awali ya wauguzi. Acha C iwe mchango wa awali wa kila muuguzi (kwa Kshs). Jumla ya pesa iliyokusudiwa kukusanywa ni Kshs 144000. Mlinganyo wa kwanza (hali ya awali): N × C = 144000 Hatua ya 2: Andika mlinganyo baada ya wauguzi kustaafu. Wauguzi 5 walistaafu, kwa hivyo idadi mpya ya wauguzi ni N - 5. Kila muuguzi aliyebaki aliongeza Kshs 2400 kwenye mchango wake, kwa hivyo mchango mpya wa kila muuguzi ni C + 2400. Jumla ya pesa iliyokusanywa bado ni Kshs 144000. Mlinganyo wa pili (hali mpya): (N - 5) × (C + 2400) = 144000 Hatua ya 3: Badilisha C kutoka mlinganyo wa kwanza hadi wa pili. Kutoka mlinganyo wa kwanza, C = 144000 / N. Badilisha hii kwenye mlinganyo wa pili: (N - 5) × (144000/N + 2400) = 144000 Hatua ya 4: Rahisisha mlinganyo kuwa fomu ya quadratic. Panua mlinganyo: 144000 + 2400N - (5 × 144000)/N - (5 × 2400) = 144000 144000 + 2400N - 720000/N - 12000 = 144000 Toa 144000 kutoka pande zote mbili: 2400N - 720000/N - 12000 = 0 Zidisha kila neno kwa N ili kuondoa sehemu: 2400N² - 720000 - 12000N = 0 Panga upya katika fomu ya kawaida ya quadratic (aN² + bN + c = 0): 2400N² - 12000N - 720000 = 0 Gawanya mlinganyo mzima kwa 2400 ili kurahisisha: N² - 5N - 300 = 0 Hatua ya 5: Tatua mlinganyo wa quadratic kwa N. Tumia fomula ya quadratic: N = [-b ± √(b² - 4ac)] / (2a) Hapa, a = 1, b = -5, c = -300. N = [ -(-5) ± √((-5)² - 4 × 1 × (-300)) ] / (2 × 1) N = [ 5 ± √(25 + 1200) ] / 2 N = [ 5 ± √(1225) ] / 2 N = [ 5 ± 35 ] / 2 Hatua ya 6: Chagua suluhisho halali kwa N. Kuna suluhisho mbili zinazowezekana: N₁ = (5 + 35) / 2 = 40 / 2 = 20 N₂ = (5 - 35) / 2 = -30 / 2 = -15 Kwa kuwa idadi ya wauguzi haiwezi kuwa hasi, tunachukua N = 20. Idadi ya awali ya wauguzi ilikuwa 20. Hatua ya 7: Kokotoa mchango wa awali wa kila muuguzi (C). Tumia mlinganyo wa kwanza: N × C = 144000 20 × C = 144000 C = 144000 / 20 C = 7200 Kila muuguzi angechangia Kshs 7200 kama wauguzi 5 wasingestaafu. Majibu ya Mwisho: a) Idadi ya awali ya wauguzi katika hospitali ya rufaa ya Nairobi ilikuwa 20. b) Kila muuguzi angechangia Kshs 7200 kwa shilingi iliyo karibu, kama wauguzi 5 wasingestaafu. Tuma swali linalofuata 📸