SOLUTION: Ron has 11 coins with a total value of $1.55. The coins are nickels and quarters. How many of each coin does he have?

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Question 992200: Ron has 11 coins with a total value of $1.55. The coins are nickels and quarters. How many of each coin does he have?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
You can either do it with 1 unknown or with 2 unknowns.
I'll do it both ways.

With 1 unknown

Let the number of nickels be x
Then the number of quarters, using
ONE PART = TOTAL MINUS OTHER PART,
is 11-x.
                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
nickels      x        $0.05    $0.05x
quarters   11-x       $0.25    $0.25(11-x)
-------------------------------------------
TOTALS      11        -----    $1.55

 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%22%28matrix%285%2C1%2CTotal%2Cvalue%2Cof%2CALL%2Ccoins%29%29

        0.05x + 0.25(11-x) = 1.55

Get rid of decimals by multiplying every term by 100:

             5x + 25(11-x) = 155

            5x + 275 - 25x = 155

                -20x + 275 = 155

                      -20x = -120

                         x = 6 = the number of nickels.

The number of quarters is 11-x or 11-6 or 5 quarters.

Checking:  6 nickels is $0.30 and 5 quarters is $1.25
            That's 11 coins.
            And indeed $0.30 + $1.25 = $1.55


---------------------
With two 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       11      -----     $1.55

 The first equation comes from the second 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 = 11

 The second equation comes from the last 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 = 1.55

Get rid of decimals by multiplying every term by 100:

                5x + 25y = 155

 So we have the system of equations:

           system%28x+%2B+y+=+11%2C5x+%2B+25y+=+155%29.

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

           x + y = 11
               y = 11 - x

Substitute (11 - x) for y in 5x + 25y = 155

  5x + 25(11 - x) = 155
   5x + 275 - 25x = 155
       -20x + 275 = 155
             -20x = -120
                x = 6 = the number of nickels.

Substitute in y = 11 - x
              y = 11 - (6
              y = 5 quarters.

The number of quarters is 11-x or 11-6 or 5 quarters.

Checking:  6 nickels is $0.30 and 5 quarters is $1.25
            That's 11 coins.
            And indeed $0.30 + $1.25 = $1.55dwin

Edwin