Let x = number of 50¢ pieces

then x-5 = number of 25¢ pieces



Expressing $32.50 in cents, we get:

50x + 25(x-5) = 3250   



Solve for x:

x = 45    = number of 50¢ pieces

x-5 = 40  = number of 25¢ pieces 

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


Using formal algebra....


let x = # of quarters

then x+5 = # of half dollars


The total value is $32.50, or 3250 cents:





Solve using basic algebra; I leave that much to you.


An informal solution using logical reasoning and easy mental arithmetic can get you to the solution faster then the formal algebra, and using very nearly the same steps.


(1) Count the "extra" five half dollars first.  That's $2.50, or 250 cents; and it leaves equal numbers of quarters and half dollars with a total value of $30, or 3000 cents.

(2) Consider groups of one quarter and one half dollar; the value of each group is 75 cents.

(3) To make the remaining 3000 cents, the number of those groups needs to be 3000/75 = 40.

(4) So there are 40 quarters and 40+5=45 half dollars.


Of course the answer you got using formal algebra should be the same.


 

Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
 .


x = # of quarters

(x+5) = # of 50-cent coins.


The total money equation


    25x + 50(x+5) = 3250  cents.


From the equation


    x =  = 40.


ANSWER.  40 quarters and 45 50-cent coins.


CHECK.  40*25 + 45*50 = 3250 cents.    ! Correct !




Solved.





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





On coin problems,  see the lessons



    - 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



    - Advanced coin problems 



    - Solving coin problems mentally by grouping without using equations



    - Non-typical coin problems 



    - Santa Claus helps solving coin problem



    - OVERVIEW of lessons on coin word problems



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  "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.









 

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