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1. You can solve this problem mentally, without using equations.
For a moment, put 5 extra quarters aside.
Then you have a collection of equal number of quarters and dimes, which worth 440 - 5*25 = 440 - 125 = 315 cents.
Since the number of quarters and dimes is the same, you can group the coins in pairs containing one dime and one quarter each.
Each group is worth 25 + 10 = 35 cents, and the number of these groups is = 9.
So, the original collection has 9 dimes and 9+5 = 14 quarters.
Check. 9*10 + 14*25 = 440 cents. ! Correct !
2. Or you can solve the problem algebraically.
Q = D + 5 (1)
25*Q + 10*D = 440. (2)
From eq(1) substitute the expression for Q into equation (2)
25*(D+5) + 10D = 440
25D + 125 + 10D = 440
35Q = 440 - 125 = 315 ====> Q = = 9.
And you obtain the same answer.
Notice that this algebraic solution simply follows and repeats the logical solution above.
Simply both methods express the same computational idea.
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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
- 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
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.