SOLUTION: A collection of dimes and nickels is worth $3.30. If there are 42 coins in all, how much of each kind of coin are there?

Question 1112925: A collection of dimes and nickels is worth $3.30. If there are 42 coins in all, how much of each kind of coin are there?
Found 3 solutions by stanbon, greenestamps, ikleyn:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
A collection of dimes and nickels is worth $3.30. If there are 42 coins in all, how much of each kind of coin are there?
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Equations:
Quantity:: d + n = 42 coins
Value:::: 10d + 5n = 330 cents
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Modify::
d + n = 42
2d + n = 66
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Subtract and solve for "d":
d = 24 (# of dimes)
n = 42-24 = 18 (# of nickels)
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Cheers,
Stan H.
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Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

Here is a quick way to find the answer to this kind of problem with a few mental calculations.

(1) If all 42 coins were dimes, the total would be $4.20, which is 90 cents more than the actual total.
(2) Each dime is worth 5 cents more than each nickel; each time a dime is replaced with a nickel, the total goes down by 5 cents.
(3) The number of nickels is 90/5 = 18.
(4) The number of dimes is 42-18 = 24.
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.
In the lesson
    - Three methods for solving standard (typical) coin word problems
in this site you will find all three methods used for solving such problems:

         1- Algebra solution,   System of 2 equations approach

         2- Algebra solution,   1 single equation approach,     and

         3- Logical analysis (MENTAL solution without using equations).

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