Question 1065120
.
A newspaper carrier has $4.60 in change. He has two more quarters than dimes but five times as many nickels as quarters. 
How many coins of each type does he have?
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<pre>
Let "q" be the number of quarters, "d" be the number of dimes and "n" be the number of nickels.

Then what you have from the condition is 

d = q - 2  and  n = 5q.      (1)

Next, you have the "value" equation

5n + 10d + 25q = 665.        (2)

Substitute (1) into the "value" equation. You will get a single equation for q:

5*(5q) + 10*(q-2) + 25q = 460.

Simplify and solve it for q:

25q + 10q - 20 + 25q = 460,

60q = 460 + 20,

60q = 480,

q = {{{480/60}}} = 8.

Now from (1)  d = q - 2  = 8 - 2 = 6  and  n = 5q = 5*8 = 40.

<U>Answer</U>.  40 nickels,  6 dimes  and  8 quarters.
</pre>

There is entire bunch of lessons on coin problems

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/coins/Coin-problems.lesson>Coin problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/coins/More-Coin-problems.lesson>More Coin problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/coins/Solving-coin-problem-without-equations.lesson>Solving coin problems without using equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/coins/Kevin-and-Randy-Muise-have-a-jar.lesson>Kevin and Randy Muise have a jar containing coins</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/coins/Typical-coin-problems-from-the-archive.lesson>Typical coin problems from the archive</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/coins/More-complicated-coin-problems.lesson>More complicated coin problems</A> (*)

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/coins/Solving-coin-problems-mentally-by-grouping-without-using-equations.lesson>Solving coin problems mentally by grouping without using equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/coins/Santa-Claus-helps-solving-coin-problem.lesson>Santa Claus helps solving coin problem</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/coins/OVERVIEW-of-lesson-on-coin-word-problems.lesson>OVERVIEW of lessons on coin word problems</A>

in this site.


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

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic "<U>Coin problems</U>".



Your problem is very similar to the problem 2 of the lesson marked (*) in the list.
For this response I simply copied and pasted that solution and updated the input data in it.