.
Let D be the number of dimes and let Q be the number of quarters.
Then from the condition, you have this system of two equations in two unknowns
D + Q = 50 coins (1) (counting coins)
10D + 25Q = 995 cents (2) (counting cents)
From equation (1), express D = 50 - Q and substitute it into equation (2).
You will get a single equation for only one unknown Q (it is how the Substitution method works) :
10*(50-Q) + 25Q = 995.
Simplify and solve this equation for Q.
500 - 10Q + 25Q = 995,
15Q = 995 - 500
15Q = 495
Q = = 33.
Thus we found the unknown Q, which is the number of quarters.
Then from equation (1) you get D = 50 - Q = 50 - 33 = 17.
It is the value of dimes.
Answer. The collection has 17 dimes and 33 quarters.
Check. 17*10 + 33*25 = 995 cents. ! Correct !
The problem is solved and the answer is checked.
Done and completed.
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It is good that the problem dictates us very stiff structure for the solution.
Now learn and memorize this solution as a mantra and repeat it EVERY TIME when you solve similar problems.
Notice that when listing the steps, the condition missed one critically important step: the solution MUST BE CHECKED at the end.
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On coin problems, see the lessons
- 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
- 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.