.
Let D be the number of dimes, and let Q be the number of quarters.
Then you have this system of 2 equations in 2 unknowns
D + Q = 28 (1) (there are 28 coins, in all)
10*D + 25*Q = 490 cents (2) (the total)
You can solve the system by different methods.
Let me call some of them: Substitution; Elimination; Cramer's rule (using determinants).
What you choose, depends on your level in Math and on your preferences.
I don't know what your level and preferences are.
So I will choose the most simple - Substitution.
From eq(1) express D = 28-Q and substitute it into eq(2), replacing D there. You will get
10*(28-Q) + 25*Q = 490
280 - 10Q + 25Q = 490
15Q = 490 - 280 = 210
Q = = 14.
Answer. 14 quarters and (the rest) 28-14 = 14 dimes.
Solved.
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There are different methods for solving such problems:
- using system of two equations (as in this post);
- using single equation in one single unknown;
- and simple logical methods without using equations.
You may learn this subject and different methods from the lesson
- Three methods for solving standard (typical) coin word problems
in this site.
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
- Non-typical coin problems
- 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.