Question 961657
Computing a percent mixture

An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 
60 grams of an alloy that contains 18% copper with 100 grams of pure copper.


Answer the questions below. Do not do any rounding.


(a) How many grams of copper are in the resulting mixture?   ____ grams


(b) What percentage of the resulting mixture is copper?    _____ %
 	

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A copper alloy is mixed with pure copper to create a new copper alloy.


There are 60 grams of the original copper alloy and it contains 18% copper.

There are 100 grams of pure (100%) copper.


(a) How many grams of copper are in the resulting mixture?


To find the amount of copper in the mixture, we first compute the amount of copper in each metal being mixed. 


Amount of copper in the alloy:   18% of 60 grams = 0.18 (60)  = 10.8 grams


Amount of copper in the pure copper:   100 grams



Then we add the amounts of copper in the metals being mixed.

10.8 grams +100 grams  =  110.8 grams


So, there are 110.8 grams of copper in the resulting mixture.


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(b) What percentage of the resulting mixture is copper?


The total amount of metal in the mixture is 60 grams +100 grams = 160 grams.


The total amount of copper in the mixture is 110.8  grams.



To determine what percentage of the mixture is copper, we first divide the total amount of copper by the total amount of metal.


     Total amount of copper in mixture
     ____________________________                      =    

     Total amount of metal in mixture



      110.8  grams  
     ___________                =     0.6925

       160 grams     



We then convert this to a percentage by multiplying by  100

(100) (0.6925)  =  69.25%


So, 69.25%  of the resulting mixture is copper.


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Here is the final answer.


(a) How many grams of copper are in the resulting mixture?      110.8  grams


(b) What percentage of the resulting mixture is copper?       69.25%