Question 1097343
.
<U>1.  Formal algebraic solution</U>


<pre>
   Q -  D   =    8      (1)    (counting coins)
25*Q + 10*D = 2370      (2)    (counting cents)


==========================>  Divide eq(2) by 5; Multiply eq(1) by 2. You will get

  2Q - 2D =  16         (3)
  5Q + 2D = 474         (4)
------------------------------Add eq(3) and eq(4)
  7Q = 490

  ========================>  Q = {{{490/7}}} = 70.


<U>Answer</U>.  70 quarters and 70-8 = 62 dimes.


<U>Check</U>.   The total is  70*25 + 62*10 = 2370 cents.   ! Correct !
</pre>


<U>2.  Light logical analysis</U>


<pre>
Put aside 8 quarters of your collection.
Then the updated collection is worth 2370 - 8*25 = 2170 cents.

But this time it consists of equal number of quarters and dimes,
and yoU can group quarters and dimes in groups (sets) in a way that each group/set contains exactly one quarter and one dime.


Thus each group is worth 25 + 10 = 35 cents,  and the number od such groups is

{{{2170/35}}} = {{{2170/70}}}.{{{2}}} = 31*2 = 62 groups.


Should I explain further that you have 62 dimes and 62+8 = 70 quarters ??


The same answer. But  <U>MENTAL</U>  solution.
</pre>

Solved.


--------------
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.


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.