Answer :
To solve this problem, we will set and solve a system of equations.
Let x be the number of nickels you have in your pocket, and y the number of dimes, then with the given information, we can set the following system of equations:
[tex]\begin{gathered} 0.05x+0.10y=0.85, \\ x+y=12. \end{gathered}[/tex]Multiplying the second equation by -0.10 and adding it to the first equation, we get:
[tex]0.05x-0.10x+0.10y-0.10y=0.85-1.2.[/tex]Solving the above equation for x, we get:
[tex]\begin{gathered} -0.05x=-0.35, \\ x=\frac{-0.35}{-0.05}, \\ x=7. \end{gathered}[/tex]Solving the second equation of the system for y, we get:
[tex]y=12-x.[/tex]Finally, substituting x=7, we get:
[tex]y=12-7=5.[/tex]