Question 912756
 – all either nickels, dimes or quarters. 

Cookie has 97 coins in her collection
<pre>
n+d+q = 97
</pre>
If 77 of her coins are quarters and dimes
<pre>
d+q=77
</pre>
And also that implies that the other 97-77 or 20 coins are nickels.
<pre>
So n = 20
</pre>
the total value of her coins is $13.95
<pre>
5n + 10d + 25q = 1395

So we have this system:

{{{system(n+d+q = 97,d+q=77,n=20,5n + 10d + 25q = 1395)}}}

Substitute n=20

{{{system(20+d+q = 97,d+q=77,20=20,5(20) + 10d + 25q = 1395)}}}

Simplify

{{{system(d+q = 77,d+q=77,100 + 10d + 25q = 1395)}}}

Simplify and delete duplicate equation:

{{{system(d+q = 77,10d + 25q = 1295)}}} 

Solve that system and get d=42,q=35

Solution: 20 nickels, 42 dimes, 35 quarters.

Edwin</pre>