SOLUTION: Your younger brother is saving up to buy an ipad. He has a total of 25 coins, all nickels and quarters.The total value is $3.85. How many nickels does he have? How many quarters? S

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Question 985545: Your younger brother is saving up to buy an ipad. He has a total of 25 coins, all nickels and quarters.The total value is $3.85. How many nickels does he have? How many quarters? Solve by using a system of equations and show all your work. Please help me with this, thank you :)
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
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       25      -----     $3.85

 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 = 25

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 = 3.85

Get rid of decimals by multiplying every term by 100:

          5x + 25y = 385

 So we have the system of equations:

          system%28x+%2B+y+=+25%2C5x+%2B+25y+=+385%29.

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

             x + y = 25
                 y = 25 - x

Substitute (25 - x) for y in 5x + 25y = 385

   5x + 25(25 - x) = 385
    5x + 625 - 25x = 385
        -20x + 625 = 385
              -20x = -240
                 x = 12 = the number of Nickels.

Substitute in y = 25 - x
              y = 25 - (12)
              y = 13 Quarters.

The number of Quarters is 25-x or 25-12 or 13 Quarters.

Checking:  12 Nickels is $0.60 and 13 Quarters is $3.25
            That's 25 coins.
            And indeed $0.60 + $3.20 = $3.85

Edwin