Question 1171536
.
<pre>

Let x be the number of nickels and

let y be the number of dimes.


Then you have these two equations

    x +   y = 40   coins      (1)    (counting for the coins)   and

   5x + 10y = 290  cents      (2)    (counting total money)


How these equations are obtained, should be totally clear.



Now, I do not know, which methods of solution of such equations you know.

So, I will show you the simplest way, using the substitution method.



From equation (1), express  x = 40-y  and substitute it into the second equation, replacing x there.  You will get

    5*(40-y) + 10y = 290.


This equation is for one unknown only, which is y.  Simplify it

    200 - 5y + 10y = 290

    -5y + 10y      = 290 - 200

       5y          = 90

        y          = 90/5 = 18.


Hence, from equation (1)

     x = 40 - 18 = 22.


<U>ANSWER</U>.  22 nickels and 18 dimes.


<U>CHECK</U>.  22*5 + 18*10 = 110 + 180 = 290 cents,  total money.   ! Correct !
</pre>

Solved.


 . . . . . . . . . . . 


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I solved the problem for you, &nbsp;using the system of two equations and the substitution method.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;There is other approach, shorter than that. &nbsp;I will show it to you, too.



<pre>
Let x be the number of nickels.

then the number of dimes is (40-x), OBVIOUSLY.


Now you can write the total money equation in this form


    5x + 10(40-x) = 290    cents.


Simplify it and find x


    5x + 400 - 10x = 290

    5x - 10x       = 290 - 400

      -5x          = -110

        x          = {{{(-110)/(-5)}}} = {{{110/5}}} = 22.


So, the number of nickels is 22;  the dimes are the rest  40-22 = 18 pieces.


Thus finally you get the same answer.
</pre>

 . . . . . . . . . . . 


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Now you know these two approaches.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;One approach starts from two equations and reduce them then to one single equation.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The other approach starts from one equation and solves it.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Which approach you select on your test, depends on how you learn the subject in the school.



I completed my post and my teaching.


You may post me, whether you do understand everything in my post and/or ask your questions.


Wish you to be successful at the test.


You may inform me about your results there.


----------------


On coin problems, &nbsp;see 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/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/Advanced-coin-problems.lesson>Advanced 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/Non-typical-coin-problems.lesson>Non-typical coin problems</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. 


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.