SOLUTION: Marlin coin bank has 31 coins consisting of nickles and quarters, worth $6.75. How many quarters are there?

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Question 1173629: Marlin coin bank has 31 coins consisting of nickles and quarters, worth $6.75. How many quarters are there?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52798)   (Show Source): You can put this solution on YOUR website!
.

Equation

     25Q + 5*(31-Q) = 675   cents.


Solution

    Q =  = 26.


ANSWER.  26 quarters and 5 nickels.


CHECK.    26*25 + 5*5 = 675 cents.    ! Precisely correct !

Solved.

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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.



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


If a formal algebraic solution is not required, you can get some good mental exercise by solving a problem like this using logical reasoning and some simple arithmetic.

(1) If all 31 coins were nickels, their value would be $1.55, which is $5.20 less than the actual value.
(2) Exchanging a nickel for a quarter keeps the total number of coins the same but increases the value by 20 cents.
(3) The number of times you need to exchange a nickel for a quarter, to make up the addition $5.20 (i.e., 520 cents), is 520/20 = 26.

So the number of quarters is 26, which leaves 5 coins to be nickels.

CHECK: 26(25)+5(5) = 650+25 = 675
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