Question 1027852
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mixing a given quantity of 30% silver alloy with a quantity of 90% silver yields 200 units of a 54% silver alloy. 
How many units of each alloy were used?
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Let x = a mass of the 30% silver alloy used, and 
    y = a mass of the 90% silver alloy used.

Then the total mass equation is 

x + y = 200,

and the "pure silver" mass equation is

0.3x + 0.9y = 0.54*200.

Simplify these equations and collect them into a system of equations

x + y  = 200,        (1)
0.3x + 0.9y = 108.   (2)

To solve it, express  x = 200 - y from  (1)  and substitute it into  (2). You will get a single equation for y:

0.3*(200 - y) + 0.9y = 108,

60 - 0.3y + 0.9y = 108,

0.6y = 108 - 60   --->   0.6y = 48   --->   y = {{{48/0.6}}} = 80.

Thus the mass of the 90% silver alloy used was 80 units.
The mass of the 30% silver alloy used was 200-80 = 120 units.
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