Answer:
[tex]63[/tex]
Step-by-step explanation:
Let number of nickels be [tex]x[/tex]
Number of dimes be [tex]y[/tex]
Number of quarters be [tex]z[/tex]
Total number of coins is [tex]185[/tex]
[tex]x+y+z=185[/tex]
Number of dimes is 5 more than quarters
[tex]y=5+z[/tex]
[tex]x+(5+z)+z=185\\\Rightarrow x+2z=180\\\Rightarrow x=180-2z[/tex]
Amount of money in the jar is $25.25
[tex]0.05x+0.1y+0.25z=25.25\\\Rightarrow 0.05x+0.1(5+z)+0.25z=25.25\\\Rightarrow 0.05x+0.5+0.1z+0.25z=25.25\\\Rightarrow 0.05x+0.35z=24.75[/tex]
[tex]0.05(180-2z)+0.35z=24.75\\\Rightarrow 9-0.1z+0.35z=24.75\\\Rightarrow 9+0.25z=24.75\\\Rightarrow z=\dfrac{24.75-9}{0.25}\\\Rightarrow z=63[/tex]
[tex]y=5+z=5+63\\\Rightarrow y=68[/tex]
[tex]x=180-2z=180-2\times 63\\\Rightarrow x=54[/tex]
So, the number of quarters is [tex]63[/tex].
