candy mix 20% chocolate to 50% Chocolate

Question

bob has a 9 pound bag of chocolate that contains 20% chocolate, how many pounds need to be removed, so when 100% chocolate is added he will have a 9 pounds of mix that contains 50% chocolate

Answer 1

We want x lbs of 100% chocolate and (9-x) lbx of 20% chocolate, giving us 9 lbs of 50% chocolate.

x + 0.2(9-x) = 0.5(9)

x + 1.8 - 0.2x = 4.5

0.8x = 2.7

x = 3.375 lbs of the 20% chocolate to be removed from the bag, replaced with 100% chocolate

There will still be 5.625 lbs of 20% chocolate in the bag; that equates to 1.125 lbs of chocolate

1.125 lbs in the bag plus the 3.375 lbs of pure chocolate added gives us 4.5 lbs of chocolate in the 9 lbs