SOLUTION: I have $5.50 total in my pocket, consisting of nickels, dimes and quarters. There are 30 coins total. There are also, 2 times as many dimes as nickels. How many of each coin do I h

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Question 779727: I have $5.50 total in my pocket, consisting of nickels, dimes and quarters. There are 30 coins total. There are also, 2 times as many dimes as nickels. How many of each coin do I have in my pocket?
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
I have $5.50 total in my pocket, consisting of nickels, dimes and quarters. There are 30 coins total. There are also, 2 times as many dimes as nickels. How many of each coin do I have in my pocket?

>>There are 30 coins total.<<
     n + d + q = 30

>>I have $5.50 total...<<
$0.05n + $0.10d + $0.25q = $5.50

    5n +    10d +    25q = 550

>>...2 times as many dimes as nickels...<<
    d = 2n

 n +   d +   q =  30
5n + 10d + 25q = 550

Substitute 2n for d in both of those:

 n +    2n  +   q =  30
           3n + q = 30

5n + 10(2n) + 25q = 550
   5n + 20n + 25q = 550
        25n + 25q = 550

Divide through by 25
         
            n + q = 22

Solve for q:

                q = 22 - n

Substitute in 

           3n + q = 30
    3n + (22 - n) = 30
      3n + 22 - n = 30
          2n + 22 = 30
               2n = 8
                n = 4

Substitute in

                q = 22 - n   
                q = 22 - 4
                q = 18

Substitute in 

                    d = 2n
                    d = 2(4)
                    d = 8

Answer:

18 quarters = 18×$0.25 = $4.50
 8 dimes    =  8×$0.10 =  0.80
 4 nickels  =  4×$0.05 =  0.20          
------------------------------
30 coins         value = %5.50

Edwin
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