SOLUTION: To meet the government's specifications, a certain alloy must be 65% aluminum. How many pounds each of a 70% aluminum alloy and a 54% aluminum alloy will be needed to produce 640 p

x pounds of the 70% alloy and the rest, (640-x) pounds of the 54% alloy.


Then the balance equation for the pure aluminium is


    0.70x + 0.54*(640-x) = 0.65*540  pounds.


From the equation, express x and calculate


    x =  = 440.


ANSWER.  440 pounds of the 70% alloy and the rest, 640-440 = 200 pounds of the 54% alloy.


CHECK.  0.70*440 + 0.54*200 = 416 pound of the pure aluminium in the ingredients, and

        0.65*640 = 416 pounds of the pure aluminium in the resulting alloy.   ! Precisely correct !