SOLUTION: A metallurgist has one alloy containing 22% copper and another containing 53% copper. How many pounds of each alloy must she use to make 51 pounds of a third alloy containing 30% c

Copper + copper      = copper

0.22*x + 0.53*(51-x) = 0.3*51  ====>

0.22x + 0.53*51 - 0.53x = 0.3*51,

-0.31x = 0.3*51 - 0.53*51 = -0.23*51  ====>  x =  =  = 37.839.


Answer.  37.839 pounds of the 22% alloy and (51-37.839) = 13.161 of the 53% alloy must be used.


Check.   0.22*37.839 + 0.53*13.161 = 15.3  pounds of copper;

         51*0.3 = 15.3 pounds of copper.    ! Correct !