Question 1195325
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An alloy is made by melting and combining two or more metals. 
A metalsmith has two alloys, each containing different amounts of silver, 
that will be melted and combined to form another alloy. 
Every 10 grams of alloy A contains 2 grams of silver, 
and every 10 grams of alloy B contains 7 grams of silver. 
To obtain 100 grams of an alloy that contains 50 grams of silver, 
how many grams of alloy A should be combined with alloy B?
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Take x times 10 grams of alloy A and y times 10 grams of alloy B.


Then the total mass equation is

    10x + 10y = 100  grams    (1)


while the pure silver mass equation is

     2x +  7y =  50  grams.   (2)


So, you have this system of 2 equations for x and y

      x +   y = 10,    (1')

     2x +  7y = 50.    (2)


From eq(1'),  express  x = 10 - y  and substitute it into equation (2).  You will get
a single equation for y

    2*(10-y) + 7y = 50

    20 - 2y  + 7y = 50

         5y       = 50 - 20

         5y       =    30

          y       =    30/5 = 6.


So, you should take 6*10 = 60 grams of alloy B and the rest, 100 - 60 = 40 grams of alloy A.   <U>ANSWER</U>


<U>CHECK</U>.  We check the content of silver. It is  7*6 + 4*2 = 42 + 8 = 50 grams.  ! Correct !
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Solved.