SOLUTION: Sam has $3.30 in quarters and dimes, and the total number of coins is 18. How many quarters and how many dimes?

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Question 1103569: Sam has $3.30 in quarters and dimes, and the total number of coins is 18. How many quarters and how many dimes?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39799)   (Show Source): You can put this solution on YOUR website!
, from quarters

, from dimes


-

10 quarters
8 dimes
Answer by ikleyn(53763)   (Show Source): You can put this solution on YOUR website!
.
  q +   d = 18,      (1)    (counting coins)
25q + 10d = 330.     (2)    (counting cents)


From eq(1), express d = 18-q and substitute it into eq(2). You will get


25q + 10*(18-q) = 330  ====>

25q + 180 - 10q = 330,

15q = 330 - 180 = 150  ====>  q =  = 10.


Answer.  10 quarters and 18-10 = 8 dimes.

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.



Answer by greenestamps(13334)   (Show Source): You can put this solution on YOUR website!


If you are looking for a fast way to find the answer, without a need to use formal algebra, then you can use logical reasoning like this....

If all 18 coins were dimes, the total value would be $1.80.
The actual value, $3.30, is $1.50 more than $1.80.
Each quarter is worth $0.15 more than each dime.
So the number of quarters is .

And 10 quarters means 8 dimes.
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