Mixture Problems

Question

A candy distributor needs to mix a 10% fat-content chocolate with a 50% fat-content chocolate to create 100 kilograms of a 22% fat-content chocolate. How many kilograms of each kind of chocolate must they use?

Answer 1

50x + 10(100-x) = 22(100)

50x -10x =22(100) -10(100)

40x = 12(100)

x = 12(100)/40 = 30

x = 30 kilos of 50% mixed with 70 kilos of 10% yield 100 kilos of 22%

50-22 = 28

22-10 = 12

28/12 = 7/3 times as much 10% as 50%

70/30 = 7/3