SOLUTION: You have 23 coins, including nickels, dimes, and quarters. If you have two more dimes than quarters, and the total value of the coins is $2.50. How many of each kind of coin do y

Question 1114360: You have 23 coins, including nickels, dimes, and quarters. If you have two more dimes than quarters, and the total value of the coins is $2.50. How many of each kind of coin do you have?
Define the variables you will be using to solve this problem.
Set up the problem by using algebraic equations to represent the problem.
Put the equations in matrix form.
q+d+n=23
D=q+2
0.25q+0.10d+0.05n=$2.50
0.25q+0.10(q+2)+0.05n=2.50
25q+10q+5n=250
35q+5n=250
I am so confused with this problem, I started to set it up and blanked. Am I even close to the algebraic equation?

Answer by ikleyn(52812) (Show Source): You can put this solution on YOUR website!
.

Your first equation is

Q + D + N = 23


Your second equation is 

D = Q + 2.


From these two equations you have

Q + (Q+2) + N = 23  

2Q + N = 21.       (1)


Now the money equation is

25Q + 10D + 5N = 250   cents,   or

25Q + 10*(Q+2) + 5N = 250,   or, equivalently

35Q + 5N = 230.    (2)


Thus you have this system of two equations in two unknowns

 2Q +  N = 21,     (1)
35Q + 5N = 230     (2)


Divide eq(2) by 5 (both sides).  Keep eq(1) as is.


 2Q + N = 21       (1')
 7Q + N = 46       (2')


Now subtract eq(1') from eq(2')

 5Q = 46 - 21 = 25  ====>  Q =  = 5.


5 quarters.  From (1')  N = 21 - 2Q = 21 - 2*5 = 11.

11 nickels.  Dimes = Q+2 = 5+2 = 7.

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.

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.

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