SOLUTION: Ann has a piggy bank with 48 coins, all of which are dimes and nickels. The total amount of money in the piggy bank is $3.90. How many more dimes are there than Nickles? A)20 B

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Question 1143710: Ann has a piggy bank with 48 coins, all of which are dimes and nickels. The total amount of money in the piggy bank is $3.90. How many more dimes are there than Nickles?
A)20
B)18
C)14
D)12a
Found 3 solutions by ikleyn, Alan3354, greenestamps:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x be the number of dimes; then the number of nickels is 48-x.


The "money" equation (also called "the value equation") is


    10x + 5*(48-x) = 390   cents.


Solve for x


    10x + 240 - 5x = 390

    10x - 5x = 390 - 240

     5x      = 150

      x      = 150/5 = 30.


Thus Ann has 30 dimes.  The rest 48-30 = 18 coins are nickels.    


30-18 = 12.


ANSWER.  There are 12 more dimes than nickels.

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If you want to learn on how to solve coin problems, look into the lesson on this subject that were written specially for you:
    - Coin problems
    - More Coin problems
    - Solving coin problems without using equations
    - Kevin and Randy Muise have a jar containing coins
    - Typical coin problems from the archive
    - Three methods for solving standard (typical) coin word problems
    - More complicated coin problems
    - Solving coin problems mentally by grouping without using equations
    - Santa Claus helps solving coin problem
    - Non-typical coin problems
    - OVERVIEW of lessons on coin word problems


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  "bird flight height"  (a top view)  is the last lesson in the list.

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
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Coin problems".


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.



Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Ann has a piggy bank with 48 coins, all of which are dimes and nickels. The total amount of money in the piggy bank is $3.90. How many more dimes are there than Nickles?
=======================
If they were all nickels, it would be $2.40 or 240 cents
Each nickel replaced by a dime add 5 cents
----
390 - 240 = 150
150/5 ---> 30 replacements by dimes.
---> 30 dimes, 18 nickels
12 more dimes
=================================
Why is anyone concerned about such a small amount of money?

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Both the informal common sense solution from tutor @alan3354 and the formal algebraic solution from tutor @ikleyn are valid; you should be able to solve problems like this by either method.

Just as a comment, though, the problem as posed can't be answered.

There are no "Nickles" in the piggy bank -- only dimes and nickels.