Question

Sarah has a collection of nickels, dimes, and quarters worth $22.25. She has 10 more dimes than nickels and twice as many quarters as dimes. How many coins of each kind does she have?

Answer 1

She has 35 dimes, 25 nickels and 70 quarters.

Explanation

Suppose, the number of dimes is $x$

As there is 10 more dimes than nickels, that means number of nickels is 10 less than dimes. So the number of nickels $=x-10$

Also, there is twice as many quarters as dimes. So, the number of quarter $=2x$

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......

$0.10x+0.05(x-10)+0.25(2x)=22.25\\ \\ 0.10x+0.05x-0.5+0.50x =22.25\\ \\ 0.65x=22.25+0.5\\ \\ 0.65x=22.75\\ \\ x=\frac{22.75}{0.65}=35$

So, the number of dimes is 35 , the number of nickels is (35-10)= 25 and the number of quarters is (2×35)= 70