SOLUTION: 29 coins all nickels and quarters in a jar sum if the coins is 4 dollars and 45 cents. how many of each coin is there?

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Question 984189: 29 coins all nickels and quarters in a jar sum if the coins is 4 dollars and 45 cents. how many of each coin is there?
Found 2 solutions by Edwin McCravy, AnlytcPhil:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of nickels be x
Then the number of quarters, using
ONE PART = TOTAL MINUS OTHER PART,
is 29-x.
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
nickels      x        $0.05    $0.05x
quarters   29-x       $0.25    $0.25(29-x)
-------------------------------------------
TOTALS      29      -----      $4.45

 The equation comes from the column on the right

  %28matrix%284%2C1%2CValue%2Cof%2CALL%2Cnickels%29%29%22%22%2B%22%22%28matrix%284%2C1%2CValue%2Cof%2CALL%2Cquarters%29%29%22=%22%22%28matrix%285%2C1%2CTotal%2Cvalue%2Cof%2CALL%2Ccoins%29%29

0.05x + 0.25(29-x) = 4.45

Get rid of decimals by multiplying every term by 100:

     5x + 25(29-x) = 445

    5x + 725 - 25x = 445

        -20x + 725 = 445

              -20x = -280

                 x = 14 = the number of nickels.

The number of quarters is 29-x or 29-14 or 15 quarters.

Checking:  14 nickels is $0.70 and 15 quarters is $3.75
            That's 29 coins.
            And indeed $0.70 + $3.75 = $4.45
Edwin

Answer by AnlytcPhil(1807) About Me  (Show Source):
You can put this solution on YOUR website!
The above solution uses only 1 unknown.  It can also be solved
using 2 unknowns.  The following uses 2 unknowns.


Let the number of nickels be x
Let the number of quarters be y
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
nickels       x       $0.05     $0.05x
quarters      y       $0.25     $0.25y
-------------------------------------------
TOTALS       29       -----     $4.45

 The first equation comes from the "number of coins" column.

  %28matrix%283%2C1%2CNumber%2Cof%2Cnickels%29%29%22%22%2B%22%22%28matrix%283%2C1%2CNumber%2Cof%2Cquarters%29%29%22%22=%22%22%28matrix%284%2C1%2Ctotal%2Cnumber%2Cof%2Ccoins%29%29

               x + y = 29

 The second equation comes from the "VALUE of all coins" column

  %28matrix%284%2C1%2CValue%2Cof%2CALL%2Cnickels%29%29%22%22%2B%22%22%28matrix%284%2C1%2CValue%2Cof%2CALL%2Cquarters%29%29%22%22=%22%22%28matrix%285%2C1%2CTotal%2Cvalue%2Cof%2CALL%2Ccoins%29%29

       0.05x + 0.25y = 4.45

Get rid of decimals by multiplying every term by 100:

            5x + 25y = 445

 So we have the system of equations:
system%28x+%2B+y+=+29%2C5x+%2B+25y+=+445%29.

We solve by substitution.  Solve the first equation for y:

  x + y = 29
      y = 29 - x

Substitute (29 - x) for y in 5x + 25y = 445

     5x + 25(29 - x) = 445
      5x + 725 - 25x = 445
          -20x + 725 = 445
                -20x = -280
                   x = 14 = the number of nickels.

     Substitute in y = 29 - x
                   y = 29 - 14
                   y = 15 quarters.

The number of quarters is 29-x or 29-14 or 15 quarters.

Checking:  14 nickels is $0.70 and 15 quarters is $3.75
            That's 29 coins.
            And indeed $0.70 + $3.70 = $4.45
Edwin