.
The number of nickels is
= 13.
The number of quarters is 13 + 11 = 24.
Explanation
Take 11 quarters from the collection, for a moment.
Then you have new/updated collection which worth (665-11*25) cents (numerator !).
In this collection the number of nickels is the same as the number of quarters,
so you can group coins of the updated collection in pairs, including one quarter and one nickels in each pair.
Then each pair worth is (5+25) cents (denominator !),
and the fraction gives you the number of pairs in the updated collection.
The rest is obvious.
There is entire bunch of lessons on coin problems
- Coin problems
- More Coin problems
- Solving coin problems without using equations
- Kevin and Randy Muise have a jar containing coins
- Typical coin problems from the archive
- More complicated coin problems
- Solving coin problems mentally by grouping without using equations
- Santa Claus helps solving coin problem
- OVERVIEW of lessons on coin word problems
in this site.
You will find there the lessons for all levels - from introductory to advanced,
and for all methods used - from one equation to two equations and even without equations.
Read them and become an expert in solution of coin problems.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Coin problems".