Question

A candy distributor needs to mix a 10% fat-content chocolate with a 40% fat-content chocolate to create 100 kilograms of a 16% fat-content chocolate. How many kilograms of each kind of chocolate must they use?

Answer 1

`x-how\ many\ kilograms\ of\ 10\%\ fat-content\ chocolate\\ \\10\%\cdot x+40\%\cdot(100-x)=16\%\cdot 100\\ \\ 0.10x+0.4(100-x)=0.16\cdot 100\\ \\0.1x+40-0.4x=16\\ \\-0.3x=-24\ /:(-0.3)\\ \\x= (24)/(0.3) \\ \\x=80\ \ \ \Rightarrow\ \ \ 100-x=100-80=20\\ \\Ans.\ 80\ kg\ -of\ 10\%\ fat-content\ chocolate;\ \\20\ kg-of\ 40\%\ fat-content\ chocolate`