Question 1105246
.
<U>1. &nbsp;&nbsp;Two equations approach</U>


<pre>
 Q = N + 5             (1)     (counting coins: "5 more quarters than nickels")
5N + 25Q = 515         (2)     (counting cents)


Next substitute (1) into eq(2). You will get

5N + 25*(N+5) = 515    (3)  ====>

5N + 25N + 125 = 515  ====>  30N = 515-125 = 390  ====>  N = {{{390/30}}} = 13.


<U>Answer</U>.  13 nickels and 13+5 = 18 quarters.


<U>Check</U>.   13*5 + 18*25 = 515 cents  ! Correct !
</pre>


<U>2. &nbsp;&nbsp;One equation approach</U>


<pre>
Let N be the number of nickels. Then the number of quarters is (N+5), according to the condition.

The "money" equation is

5N + 25*(N+5) = 515   cents    - exactly as the equation (3)  above.


The solution and the answer are the same as in the part 1.
</pre>


<U>3. &nbsp;&nbsp;Logical analysis without using equation/equations</U>


<pre>
For a minute, take away (mentally) 5 quarters from the collection.

Then you have equal number of nickels and quarters in the updated collection which is worth 515-5*25 = 390 cents now.


You can group the coins in the updated collection in the sets consisting of 1 nickel and one quarter each.


Each set is worth 25+5 = 30 cents and the number of sets is {{{390/30}}} = 13.


Then it is clear that the original collection counts 13 nickels and 13+5 = 18 quarters.
</pre>

Solved.


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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.
Pay special attention to the lesson marked (*) in the list - it is the TWIN to this solution.



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.