Question 1059482
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 Yoko has 4.60 dollars in quarters and nickels. She has 24 coins all together. How many of each coin does she have?
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<pre>
Let "n" be the number of nickels.
Then the number of quarters is (24-n).

The nickels contribute 5n cents in total.
The quarters contribute 25*(24-n) cents in total.
Altogether, the 24 coins is worth 5n + 25*(24-n).

Therefore, the equation is

5n + 25*(24-n) = 460   (cents).

Simplify and solve:

5n + 600 - 25n = 460,

-20n = 460 - 600,

-20n = -140,

n = {{(-140)/(-20)}}} = 7.

<U>Answer</U>. There are 7 nickels and 24-7 = 17 quarters in the collection.

<U>Check</U>.   7*5 + 17*25 = 460.  OK.
</pre>

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For coin problems and their detailed solutions see the lessons in this site:

&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/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>


Read them attentively and become an expert in this field.


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>".