SOLUTION: A stack of dimes and a stack of quarters total $6.80 in value. There are a total of 41 coins. Determine the number of dimes and the number of quarters in the stacks.

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Question 1029975: A stack of dimes and a stack of quarters total $6.80
in value. There are a total of 41 coins. Determine the
number of dimes and the number of quarters in the
stacks.
Found 2 solutions by Edwin McCravy, josmiceli:
Answer by Edwin McCravy(20060)   (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       41      -----       $6.80

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

  

                 x + y = 41

 The second equation comes from the last column.
  

         0.10x + 0.25y = 6.80

Get rid of decimals by multiplying every term by 100:

             10x + 25y = 680

 So we have the system of equations:
           .

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

                 x + y = 41
                     y = 41 - x

Substitute (41 - x) for y in 10x + 25y = 680

      10x + 25(41 - x) = 680
      10x + 1025 - 25x = 680
           -15x + 1025 = 680
                  -15x = -345
                     x = 23 = the number of dimes.

Substitute in y = 41 - x
              y = 41 - (23
              y = 18 quarters.

Checking:  23 dimes is $2.30 and 18 quarters is $4.50
            That's 41 coins.
            And indeed $2.30 + $4.50 = $6.8

Edwin
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let = number of dimes
Let = number of quarters
----------------------------
(1)
(2) ( in cents )
-------------------------
Multiply both sides of (1) by
and subtract (1) from (2)
(2)
(1)
-----------------------


and
(1)
(1)
----------------
There are 23 dimes and 18 quarters
----------------
check:
(2)
(2)
(2)
(2)
OK
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