SOLUTION: In a collection box, there are dimes and quarters whose total value is $28. if there were as many quarters as there are dimes, and as many dimes as there are quarters, the total

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Question 1010904: In a collection box, there are dimes and quarters whose total value is $28. if there were as many quarters as there are dimes, and as many dimes as
there are quarters, the total value would be $36.46. How many coins
of each kind are in the collection box?
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
Your $36.46 was a typo, because you'd have to have 
some pennies to get that. So I'll change your $36.46 
to $36.40.

Let D = the number of dimes
Let Q = the number of quarters 

$0.10D + $0.25Q = $28.00   <--There are D dimes and Q quarters.
$0.25D + $0.10Q = $36.40   <--if there were D quarters and Q dimes

Divide the second equation through by 5

10D + 25Q = 2800
 5D +  2Q =  728

Multiply the second equation through by -2
And add them to eliminate D

 10D + 25Q =  2800
-10D -  4Q = -1456
------------------
       21Q =  1344
         Q =  64

Substitute in 
 
  5D +  2Q =  728
5D + 2(64) = 728
  5D + 128 = 728
        5D = 600
         D = 120

64 Quarters and 120 Dimes

Checking:

64 Quarters is worth 64($0.25) = $16.00
120 Dimes is worth 120($0.10)  = $12.00
----------------------------------------
                         TOTAL = $28.00

120 Quarters is worth 120($0.25) = $30.00
64 Dimes is worth 64($0.10)      = $ 6.40
-----------------------------------------
                           TOTAL = $36.40

Edwin