She has 35 dimes, 25 nickels and 70 quarters.
Explanation
Suppose, the number of dimes is [tex]x[/tex]
As there is 10 more dimes than nickels, that means number of nickels is 10 less than dimes. So the number of nickels [tex]=x-10[/tex]
Also, there is twice as many quarters as dimes. So, the number of quarter [tex]=2x[/tex]
We know that, value of each dime, nickel and quarter are $0.10 , $0.05 and $0.25
The total value of all coins is given as $22.25 So, the equation will be......
[tex]0.10x+0.05(x-10)+0.25(2x)=22.25\\ \\ 0.10x+0.05x-0.5+0.50x =22.25\\ \\ 0.65x=22.25+0.5\\ \\ 0.65x=22.75\\ \\ x=\frac{22.75}{0.65}=35[/tex]
So, the number of dimes is 35 , the number of nickels is (35-10)= 25 and the number of quarters is (2×35)= 70
