Let x be the number of kilograms of 10% fat content chocolate and y be the number of kilograms of 50%, then we can set the following system of equations:
[tex]\begin{gathered} x+y=100, \\ 0.1x+0.5y=100\cdot0.38=38. \end{gathered}[/tex]Solving the first equation for x we get:
[tex]x=100-y\text{.}[/tex]Substituting x=100-y in the second equation and solving for y we get:
[tex]\begin{gathered} 0.1(100-y)+0.5y=38, \\ 10-0.1y+0.5y=38, \\ 0.4y=28, \\ y=70. \end{gathered}[/tex]Substituting y=70 in the third equation we get:
[tex]\begin{gathered} x=100-70, \\ x=30. \end{gathered}[/tex]Answer: They must use 30 kilograms of 10% fat content chocolate and 70 kilograms of 50% fat content chocolate.
