Please help me to solve this maths question

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.