Let "D" be the number of dimes.
Then the number of quarters is (66-D).
The dimes contribute 10*D cents to the total.
The quarters contribute 25*(66-D).
The total is 1155 cents, and the "value equation" is
10*D + 25*(66-D) = 1155.
Simplify and solve for D:
10*D + 25*66 - 25D = 1155,
10D + 1650 - 25D = 1155,
-15D = 1155 - 1650,
-15D = 495,
D = = 33.
Answer. 33 dimes and 66-33 = 33 quarters.
Check. 33*10 + 33*25 = 1155 cents = $11.55.
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.