Question 1059667
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Ana has a piggy bank that contains nickels, dimes, and quarters. When she opens the bank and counts her money, she has $3.35. 
She counted twice as many nickels as quarters, and two more dimes than quarters. How many dimes does she have?
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<pre>
Let "x" be the number of quarters in the collection.
Then the number of nickels is 2x and the number of dimes is (x+2), according to the condition.

The nickel contribute   5*(2x)    cents to the total.
The dimes contribute    10*(x+2)  cents to the total.
the quarters contribute  25x      cents to the total.

The total is 5*(2x) + 10*(x+2) + 25x.

Hence, the "value" equation is

5*(2x) + 10*(x+2) + 25x = 335.

Simplify and solve for x:

10x + 10x + 20 + 25x = 335,

45x = 335 - 20,

45x = 315  --->  x = {{{315/45}}} = 7.


<U>Answer</U>.  7 quarters, 2*7 = 14 nickels, 7 + 2 = 9 dimes.

<U>Check</U>.   7*25 + 14*5 + 9*10 = 335 cents. Correct.
</pre>

<U>The lesson to learn from this solution</U>:


1.  &nbsp;First choose the major unknown reasonably.


2.  &nbsp;Second, express other unknowns via the major unknown.


3.  &nbsp;Then make an equation.


4.  &nbsp;Then solve the equation.


It is your algorithm.



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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/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.


Read them and become an expert in solution of coin problems.


Also, 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>".