.
1. Two equations approach
Q = N + 5 (1) (counting coins: "5 more quarters than nickels")
5N + 25Q = 515 (2) (counting cents)
Next substitute (1) into eq(2). You will get
5N + 25*(N+5) = 515 (3) ====>
5N + 25N + 125 = 515 ====> 30N = 515-125 = 390 ====> N = = 13.
Answer. 13 nickels and 13+5 = 18 quarters.
Check. 13*5 + 18*25 = 515 cents ! Correct !
2. One equation approach
Let N be the number of nickels. Then the number of quarters is (N+5), according to the condition.
The "money" equation is
5N + 25*(N+5) = 515 cents - exactly as the equation (3) above.
The solution and the answer are the same as in the part 1.
3. Logical analysis without using equation/equations
For a minute, take away (mentally) 5 quarters from the collection.
Then you have equal number of nickels and quarters in the updated collection which is worth 515-5*25 = 390 cents now.
You can group the coins in the updated collection in the sets consisting of 1 nickel and one quarter each.
Each set is worth 25+5 = 30 cents and the number of sets is = 13.
Then it is clear that the original collection counts 13 nickels and 13+5 = 18 quarters.
Solved.
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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.
Pay special attention to the lesson marked (*) in the list - it is the TWIN to this solution.
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.