Maths question

(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
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(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
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(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
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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