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(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.

Equation

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


Solution

    Q = %28675-5%2A31%29%2F%2825-5%29 = 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
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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.

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    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

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


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Free of charge online textbook in ALGEBRA-I
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to your archive and use it when it is needed.



Answer by greenestamps(13200) About Me  (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