SOLUTION: Sally has $4.55 in dimes and quarters. If she has 23 coins in all, how many dimes does she have?

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Question 1003305: Sally has $4.55 in dimes and quarters. If she has 23 coins in all, how many dimes does she have?
Answer by Edwin McCravy(20060) 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       23        -----    $4.55

 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 = 23

 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 = 4.55

Get rid of decimals by multiplying every term by 100:

          10x + 25y = 455

 So we have the system of equations:
           system%28x+%2B+y+=+23%2C10x+%2B+25y+=+455%29.

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

           x + y = 23
               y = 23 - x

Substitute (23 - x) for y in 10x + 25y = 455

     10x + 25(23 - x) = 455
      10x + 575 - 25x = 455
           -15x + 575 = 455
                 -15x = -120
                    x = 8 = the number of dimes.

Substitute in y = 23 - x
              y = 23 - (8
              y = 15 quarters.

The number of quarters is 23-x or 23-8 or 15 quarters.

Checking:  8 dimes is $0.80 and 15 quarters is $3.75
            That's 23 coins.
            And indeed $0.80 + $3.75 = $4.55


 So it checks.  8 dimes and 15 quarters
Edwin