Question 1099460
.
A child’s piggy bank contains 35 coins and a total of  $6.25.  The bank contains quarters, dimes and nickels.  
There are twice as many dimes as there are nickles.  How many of each coin is in the bank? 
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<pre>
Let N be the number of nickels.

Then the number of dimes is 2N, according to the condition.

Hence, the number of quarters is (35-N-2N) = (35-3N).


The nickels contribute  5N             cents towards the total.

The dimes contribute    10*(2N) = 20N  cents towards the total.

The quarters contribute 25*(35-3N)     cents towards the total.


So, your balance equation is

5N + 20N + 25*(35-3N) = 625  cents.    (<<<---===  you counted all the cents)


Simplify and solve for N step by step.

25N + 875 - 75N = 625  ====>  -50N = 625 - 875 = -250  ====>  N = {{{(-250)/(-50)}}} = 5.


<U>Answer</U>. 5 nickels,  10 dimes and 35-5-10 = 20 quarters.


<U>Check</U>.  Can you check it on your own ??
</pre>


<U>The lesson to learn from this solution</U>:

<pre>
    This problem is FOR ONE UNKNOWN.

    Therefore, I made all efforts from my side to solve it as the problem in ONE UNKNOWN.
</pre>


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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/Three-methods-for-solving-standard-typical-coin-problem.lesson>Three methods for solving standard (typical) coin word problems</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.


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, &nbsp;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>".



Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.