Question 238040
Let n= number of nickels
d= number of dimes
q=number of quarters

We have 3 unknowns, so we need to make 3 equations from the given information.

Eqn 1: {{{n + d + q=50}}}
Eqn 2: {{{0.05*n+0.10*d + 0.25*q=5.60}}}
Eqn 3: {{{0.10*d=5*0.05*n}}}

We then need to isolate two of the variables. I will choose to isolate for d in Eqn 3:

{{{0.10*d=5*0.05*n}}}
{{{d=5*0.05*n/0.10}}}
{{{d=2.5n}}}

And q in Eqn 1:

{{{n + d + q = 50}}}
{{{q=50 - n - d}}}

Now substitute the value of d = 2.5n into Eqn 1:

{{{q=50 - n - 2.5n}}}
{{{q=50 - 3.5n}}}

Now we have d in terms of n (d=2.5n), and q in terms of n (q=50-3.5n).

We can now substitute these into Eqn 2:

Eqn 2: 
{{{0.05*n+0.10*d + 0.25*q = 5.60}}}
{{{0.05*n+0.10*(2.5n) + 0.25*(50-3.5n)=5.60}}}

Distributing:
{{{0.05*n+0.25n) + 12.5-0.875n=5.60}}}

Collecting like terms:
{{0.3n-0.875n=12.60-5.60}}}
{{{0.575n=6.9}}}

Divide both sides by 0.575:
{{{n=12}}}

We can then use this to find d:

d=2.5n
d=2.5(12)
d=30

We can also now find q:

q=50-3.5n
q=50-3.5(12)
q=50-42
q=8

So there are 12 nickels, 30 dimes, and 8 quarters.