.
Solution
= = 36 dimes
and 60 - 36 = 24 nickels.
Check. 24*5 + 36*10 = 480 cents. ! Correct !
Explanation
Let assume for a minute that ALL 60 coins of the collection are nickels.
Then the collection would worth 5*60 = 300 cents.
But it is worth by 180 = 480-300 cents more.
Why there is this difference ? - But of course, the difference is due to the fact that I counted 10-cent dimes as 5-cent nickels.
So, divide this difference of 180 cents by the difference 10-5 = 5 cents, and you will get the number of dimes.
It is exactly what my formula shows at the very beginning of my post.
Solved. It is the way to solve the problem MENTALLY without using equations.
---------------
There is entire bunch of lessons on coin problems
- 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
- 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.
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.