SOLUTION: word problem in algebra Denise has a collection of 16 coins consisting of dimes and quarters. The total value of all her coins is $3.25. How many dimes does she have? Dimes

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Question 1114230: word problem in algebra
Denise has a collection of 16 coins consisting of dimes and quarters. The total value of all her coins is $3.25. How many dimes does she have?
Dimes=10x
quarters=25x
total value=325
and I'm stumped with the rest. thank you for helping me.

Found 2 solutions by ikleyn, stanbon:
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website!
.
Your start is INCORRECT.   The correct and full solution is below.

D + Q = 16 (1) (counting coins) 10D + 25Q = 325 (2) (counting cents) From equation (2), express Q = 16-D and substitute it into equation (2), replacing Q. You will get a SINGLE equation for only one unknown 10*D + 25*(16-D) = 325 10D + 400 - 25D = 325 -15D = 325 - 400 = -75 ====> D = = 5. Answer. 5 dimes and 16-5 = 11 quarters. Check. 5*10 + 11*25 = 325 cents ! Correct !

Solved.

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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
    - 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.

Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website!
Denise has a collection of 16 coins consisting of dimes and quarters. The total value of all her coins is $3.25. How many dimes does she have?
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Equations:
Quantity:: d + q = 16 coins
Value:: 10d 25q = 325 cents
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Get rid of the q's::
25d + 25q = 25*16
10d + 25q = 325
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Subtract and solve for "d"::
15d = 75
d = 5 (# of dimes)
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Cheers,
Stan H.
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