SOLUTION: A man has 30 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 465 cents, how many dimes and how many quarters does he have?

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Question 1017226: A man has 30 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 465 cents, how many dimes and how many quarters does he 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       30      -----     $4.65

 The first equation comes from the second 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 = 30

 The second equation comes from the last 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

           0.1x + 0.25y = 4.65

Get rid of decimals by multiplying every term by 100:

              10x + 25y = 465

 So we have the system of equations:
           system%28x+%2B+y+=+30%2C10x+%2B+25y+=+465%29.

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

              x + y = 30
                  y = 30 - x

Substitute (30 - x) for y in 10x + 25y = 465

   10x + 25(30 - x) = 465
    10x + 750 - 25x = 465
         -15x + 750 = 465
               -15x = -285
                  x = 19 = the number of dimes.

Substitute in y = 30 - x
              y = 30 - (19
              y = 11 quarters.

Checking:  19 dimes is $1.90 and 11 quarters is $2.75
            That's 30 coins.
            And indeed $1.90 + $2.75 = $4.65
Edwin