Answer
$15$ nickels.
$10$ dimes.
$5$ quarters.
Work Step by Step
Write a system of equations to solve for the three variables, $n$, $d$, and $q$ based on the problem.
$5n+10d+25q=300$
$d=2q$
$5+d=n$
And now we will manipulate the third equation.
$5+d=n$
$d=n-5=2q$
$n=2q+5$
Plug these into the first equation to solve for $q$.
$5(2q+5)+10(2q)+25q=300$
$(2q+5)+2(2q)+5q=60$
$11q+5=60$
$q=\frac{60-5}{11}=\frac{55}{11}=5$
Substitute this value for $q$ into the other equations.
$n=2q+5=2(5)+5=15$
$d=2q=2(5)=10$
