SOLUTION: you have $13.80 in quarters and dimes. if you have 84 coins, how many are dimes?

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Question 1010672: you have $13.80 in quarters and dimes. if you have 84 coins, how many are dimes?

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number of quarters be x
Let the number of dimes be y


                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
coin        coins      coin      coins
-------------------------------------------
quarters     x        $0.25     $0.25x
dimes        y        $0.10     $0.10y
-------------------------------------------
TOTALS      84       -----      $13.80

 The first equation comes from the second column.

  %28matrix%283%2C1%2CNumber%2Cof%2Cquarters%29%29%22%22%2B%22%22%28matrix%283%2C1%2CNumber%2Cof%2Cdimes%29%29%22%22=%22%22%28matrix%284%2C1%2Ctotal%2Cnumber%2Cof%2Ccoins%29%29

                 x + y = 84

 The second equation comes from the last column.
  %28matrix%284%2C1%2CValue%2Cof%2CALL%2Cquarters%29%29%22%22%2B%22%22%28matrix%284%2C1%2CValue%2Cof%2CALL%2Cdimes%29%29%22%22=%22%22%28matrix%285%2C1%2CTotal%2Cvalue%2Cof%2CALL%2Ccoins%29%29

           0.25x + 0.10y = 13.80

Get rid of decimals by multiplying every term by 100:

               25x + 10y = 1380

 So we have the system of equations:
           system%28x+%2B+y+=+84%2C25x+%2B+10y+=+1380%29.

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

           x + y = 84
               y = 84 - x

Substitute (84 - x) for y in 25x + 10y = 1380

   25x + 10(84 - x) = 1380
    25x + 840 - 10x = 1380
          15x + 840 = 1380
                15x = 540
                  x = 36 = the number of quarters.

Substitute in y = 84 - x
              y = 84 - (36
              y = 48 dimes.

Checking:  36 quarters is $9.00 and 48 dimes is $4.80
            That's 84 coins.
            And indeed $9.00 + $4.80 = $13.80
Edwin