Question 1144063
.


            There are several different Algebra approaches.


            Two of them  are presented below -- the most popular among beginner students.



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>One equation setup</U>


<pre>
Let x be the number of the $20 coins.

Then the number of $20 coins is (47-x).


Then the "face value equation" is


    20x + 10*(47-x) = 700   dollars.


From the equation, express x and calculate


    x = {{{(700 - 10*47)/(20-10)}}} = 23.


<U>ANSWER</U>.  23 coins are the $20 coins and the rest 47-23 = 24  are the $10 coins. 


<U>CHECK</U>.   23*20 + 24*10 = 700 dollars.   ! Correct !
</pre>


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>Two equations setup</U>


<pre>
Let x be the number of the $20 coins, and

let y be the number of $10 coins.


From the condition, you have these two equations


    x  +   y =  47   coins       (2)

   20x + 10y = 700   dollars.    (3)


From the first equation, express  y = 47-x  and substitute it into the second equation.


You will get an equation for single unknown


    20x + 10*(47-x) = 700.      (4)


Equation (4) is identical to equation (1).
Therefore, the rest of solution is the same as in the first method, giving (of course) the same answer.
</pre>


There are also other logical methods of solution without using equations -- see the lesson &nbsp;(*) &nbsp;in the list below.


All these methods are presented in the lessons

&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/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/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=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. 


A convenient place to quickly observe these lessons from a &nbsp;"bird flight height" &nbsp;(a top view) &nbsp;is the last lesson in the list.


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.