Question 1121178
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<pre>
You can start from the system of two equations in two unknowns


 x +   y =  24       (1)     (counting coins)
5x + 25y = 240       (2)     (counting cents)


Then you can multiply the first equation by 5 (both sides) to get the system in the equivalent form


5x +  5y = 120       (1')
5x + 25y = 240       (2')


Now you can subtract equation (1') from equation (2'). In this way, you exclude the unknown x, and you get

a single equation for the unknown y:

25y - 5y = 240 - 120

20y = 120

y = {{{120/20}}} = 6.


<U>Answer</U>.  6 quarters and  (24-6) = 18 nickels.


<U>Check</U>.   6*25 + 18*5 = 240  cents.   ! Correct !
</pre>

Solved.    &nbsp;&nbsp;&nbsp;&nbsp;// &nbsp;&nbsp;The method I used to solve the system is called the "Elimination method".


So, &nbsp;on the way, &nbsp;you learned how to solve the system of equations using the Elimination method.


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


For coin problems and their detailed solutions see the lessons in this site:

&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>


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 attentively and become an expert in this field.


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.