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Maths question

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1. The ratios of the weights of zinc and copper in two alloys A and B are 2:3 and 1:4 respectively. Alloy A, x kg and alloy B, y kg are melted to yeild a new alloy containing 75% of copper.(a) Find the weights of zinc and copper in terms of x and y.(b) Hence or otherwise, find the ratio x:y.(c) Further, if... 顯示更多 1. The ratios of the weights of zinc and copper in two alloys A and B are 2:3 and 1:4 respectively. Alloy A, x kg and alloy B, y kg are melted to yeild a new alloy containing 75% of copper. (a) Find the weights of zinc and copper in terms of x and y. (b) Hence or otherwise, find the ratio x:y. (c) Further, if the weight of the new alloy is 10kg, find the weight of copper from alloy A.

最佳解答:

(a) zinc Copper Alloy A 2x/5 3x/5 Alloy B 1y/5 4y/5 the weights of zinc is ( 2/5x + 1/5 y ) kg and the weights of copper ( 3/5x + 4/5 y ) kg ============================================================= (b) , The weight of ht enew alloy should be (x+y) kg As a new alloy containing 75% (i.e. 3/4 )of copper hence, 3/5x + 4/5 y = 3(x+y)/4 3x = y so, x: y = 1: 3 ============================================================= (c) As the weight of the new alloy is 10kg Hence, x + y = 10 x + 3x = 10 ( subsutitute y= 3x , result from (b)) x= 2.5 then y= 3x=3 x 2.5 = 7.5 So the weight of copper from alloy A is 3x/5 = 3 ( 2.5) /5 = 1.5 kg ===============================================================

其他解答:

The ratios of the weights of zinc and copper in alloy A is 2:3 The ratios of the weights of zinc and copper in alloy B is 3:12 (=1:4) The ratios of the weights of zinc and copper in new alloy is 5:15 or (1:3) so if alloy A is 1kg, alloy B will be 3kg because [(1:4)x3 = (3:12)] (a) the weights of zinc and copper in terms of x and y are 1kg and 3kg (b) the ratio xy is 1:3 if the weight of the new alloy is 10kg, the weight of alloy A is 2.5kg. the weight of alloy B is 7.5kg because 10kg /4 x1 = 2.5kg and 10kg /4 x3 = 7.5kg (c) if the weight of the new alloy is 10kg, the weight of copper from alloy A is . 1kg / 5 x 3 = 600g or 0.6kg
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