標題:
Please help me to solve this maths question
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發問:
There are 62 kg of metal A and 55kg of metal B.They are melted to form two alloys,one containing 64% metal A and one containing 33/1/3% matal A.What weight of each alloy should be preduced so that no metal will be left? 運算步驟加答案
最佳解答:
Let the weight of metal A in alloy P be a kg.; Therefore, the weight of metal A in alloy Q will be (62 - a) kg.; Let the weight of metal B in alloy P be b kg.; Therefore, the weight of metal B in alloy Q will be (55 - b) kg.; For alloy P, a / (a + b) = 64%; 100a = 64 a + 64b; b = 36a / 64 b = 9/16 a..........(i) For alloy Q, (62 - a) / [(62 - a) + (55 - b)] = (33 1/3 %) ; 62 - a = [117 - a - b] ( 1/3); 186 - 3a = 117 - a - b; 2a - b = 69..........(ii) Put b= 9/16 a....(i) into (ii), we get 2a - 9/16 a = 69; 23/16 a = 69 a = 48 (kg.) (Ans.); From (i), b = 9 / 16 a; b = 9 / 16 * 48; b = 27 (kg.) (Ans.) I hope I can help. 2007-03-06 21:27:20 補充： Continued:For alloy Q, weight of metal A = 62 - a = 62 - 48 = 14 (kg.);For alloy Q, weight of metal B= 55 - b = 55 - 27 = 28 (kg.);That is,Alloy P has 48 kg. of metal A and 27kg. of metal B; andalloy Q has 14 kg. of metal A and 28 kg. of metal B. 2007-03-07 13:50:16 補充： O.K. 嗎? 2007-03-07 17:51:57 補充： That is,75 kg. of Alloy P comprising 48 kg. of metal A and 27 kg. of metal B;and 42 kg. of Alloy Q comprsing 14 kg. of metal and 28 kg. of metal B, should be produced. 2007-03-07 18:27:17 補充： Correction !!!!Let the weight of metal A in alloy P be a kg.;Let the weight of metal B in alloy P be b kg.;Thus, the weight of metal A in alloy Q will be (62 - a) kg.;Thus, the weight of metal B in alloy Q will be (55 - b) kg.; 2007-03-07 18:28:37 補充： Correction continued-For alloy P, a / (a b) = 64%;100a = 64a 64b;36/64 a = b….(i);For alloy Q, (62 – a) / [(62 – a) (55 – b)] = 33 1/3 % ;3 * 62 – 3 * a = 117 – a – b;186 – 3a = 117 – a – b;69 = 2a – b……(ii); 2007-03-07 18:29:29 補充： Correction continued-Put 36/64 a = b into (ii), we get69 = 2a - 36/64 a;69 = 92 / 64 a;a = 48;From (ii), 69 = 2 * 48 – b;b = 27; 2007-03-07 18:30:19 補充： Correction continued-Thus,a b = 48 27 = 75;(62 – a) = 62 – 48 = 14;(55 – b) = 55 – 27 = 28;(62 – a) (55 – b) = 62 – 48 55 – 27 = 42; 2007-03-07 18:30:58 補充： Ans. The weight of alloy P is 75 kg. comprising 48 kg. of metal A and 27 kg. of metal B; and the weight of alloy Q is 42 kg. comprising 14 kg. of metal A and 28 kg. of metal B.
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