Let the number of nickels be = n
Let the number of dimes be = d
Let the number of quarter be = q
Total money William has = $12.80
As given, there are 3 times as many quarters as nickels
[tex]q=3n[/tex]
And 20 more dimes than nickels
[tex]d=20+n[/tex]
As total money is $12.80
[tex]0.05n+0.10d+0.25q=12.80[/tex]
Putting the values of 'q' and 'd' to find 'n'
[tex]0.05n+0.10(20+n)+0.25(3n)=12.80[/tex]
[tex]0.05n+2+0.10n+0.75n=12.80[/tex]
[tex]0.90n+2=12.80[/tex]
[tex]0.90n=10.80[/tex]
[tex]n=12[/tex]
Hence the number of nickels are = 12
If you want to also find dime and quarter, then
[tex]q=3n=3\times12=36[/tex]
[tex]d=20+n=20+12=32[/tex]
