SOLUTION: A bag contains a total of 200 quarters and dimes. If the total value of the bags contents is $41.00.How many quarters and how many dimes are in the bag?

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Question 1092135: A bag contains a total of 200 quarters and dimes. If the total value of the bags contents is $41.00.How many quarters and how many dimes are in the bag?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52814)   (Show Source):
You can put this solution on YOUR website!
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25Q + 10*(200-Q) = 4100 cents ====> 25Q + 20000 - 10Q = 4100 ====> 15Q = 4100 - 2000 = 2100 ====> Q = = 140. Answer. 140 quarters and 200-140 = 60 dimes.

Solved.

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For coin problems and their detailed solutions see the lessons in this site:
    - 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
    - Solving coin problems mentally by grouping without using equations
    - Santa Claus helps solving coin problem

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.

Read them attentively and become an expert in this field.

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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Notice, that what the tutor @greenestamps explained to you, was also described in the lesson marked (*) in my list of lessons.

Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!

Here is a solution that combines informal algebra with logical analysis... instead of using purely formal algebra.

Suppose all 200 coins were quarters. The total value would be $50.

But the total is only $41. That's $9 short of the total we would get with all quarters.

So let's start taking away quarters and replacing them with dimes. Each time we do that, the total value of the coins is reduced by 15 cents -- because the quarter was worth 25 cents and we replaced it with a dime worth only 10 cents.

But if we need to get the $50 down to $41, we need to reduce the value of the coins by $9, or 900 cents. If each time we replace a quarter with a dime we reduce the total value by 15 cents, then the number of quarters we need to replace is 900/15 = 60.

And when we have replaced 60 quarters with dimes, we find we have 140 quarters and 60 dimes.