SOLUTION: Barbara has some dimes and quarters. If she has 25 coins worth a total of $2.95, how many of each type of coin does she have?

Question 1054128: Barbara has some dimes and quarters. If she has 25 coins worth a total of $2.95, how many of each type of coin does she have?
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!

Let the number of dimes be x
Let the number of quarters be y


                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
dimes         x      $0.10     $0.10x
quarters      y      $0.25     $0.25y
-------------------------------------------
TOTALS       25      -----     $2.95

 The first equation comes from the second column.

  
             
                  x + y = 25

 The second equation comes from the last column.
  

          0.10x + 0.25y = 2.95

Get rid of decimals by multiplying every term by 100:

              10x + 25y = 295

 So we have the system of equations:
           .

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

                  x + y = 25
                      y = 25 - x

Substitute (25 - x) for y in 10x + 25y = 295

       10x + 25(25 - x) = 295
        10x + 625 - 25x = 295
             -15x + 625 = 295
                   -15x = -330
                      x = 22 = the number of dimes.

        Substitute in y = 25 - x
                      y = 25 - (22)
                      y = 3 quarters.


Checking:  22 dimes is $2.20 and 3 quarters is $0.75

            That's 25 coins.

And indeed $2.20 + $0.75 = $2.95

Edwin

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