Answer:
[tex]Nickels: 13\\\\Half\ dollars:9[/tex]
Step-by-step explanation:
Let be "n" the number of nickels the boy has in the cash box and "h" the number of half dollars the boy has in the cash box.
Set up a system of equations:
[tex]\left \{ {{n+h=22} \atop {0.05n+0.5h=5.15}} \right.[/tex]
You can use the Elimination method to solve the system. Multiply the first equation by -0.5, add both equations and then solve for "n":
[tex]\left \{ {{-0.5n-0.5h=-11} \atop {0.05n+0.5h=5.15}} \right.\\...........................\\-0.45n=-5.85\\\\n=\frac{-5.85}{-0.45}\\\\n=13[/tex]
Finally, substitute the value of "n" into the first equation and solve for "h":
[tex]13+h=22\\\\h=22-13\\\\h=9[/tex]
