SOLUTION: Luz has 37 coins in her purse. Some are dimes and the rest are quarters. The value of the coins is $5.95. How many dimes does she have?

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Question 1037964: Luz has 37 coins in her purse. Some are dimes and the
rest are quarters. The value of the coins is $5.95.
How many dimes does she have?
Answer by Edwin McCravy(20056) About Me  (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       37      -----       $5.95

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

  %28matrix%283%2C1%2CNumber%2Cof%2Cdimes%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 = 37

 The second equation comes from the "Value of all coins" column.
  %28matrix%284%2C1%2CValue%2Cof%2CALL%2Cdimes%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

         0.10x + 0.25y = 5.95

Get rid of decimals by multiplying every term by 100:

             10x + 25y = 595

 So we have the system of equations:
           system%28x+%2B+y+=+37%2C10x+%2B+25y+=+595%29.

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

                 x + y = 37
                     y = 37 - x

Substitute (37 - x) for y in 10x + 25y = 595

      10x + 25(37 - x) = 595
       10x + 925 - 25x = 595
            -15x + 925 = 595
                  -15x = -330
                x = 22 = the number of dimes.

Substitute in y = 37 - x
              y = 37 - (22)
              y = 15 quarters.

Checking:  22 dimes is $2.20 and 15 quarters is $3.75
            That's 37 coins.
            And indeed $2.20 + $3.75 = $5.95
Edwin