SOLUTION: Harry has $6.10 in his pocket. He has twice as many quarters as nickels and one more dime than quarters. How many of each coin does Harry have

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Question 1052972: Harry has $6.10 in his pocket. He has twice as many quarters as nickels and one more dime than quarters. How many of each coin does Harry have
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
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Harry has $6.10 in his pocket. He has twice as many quarters as nickels and one more dime than quarters.
How many of each coin does Harry have
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

For a moment, take off one dime from the collection (mentally).

Then you can group the remaining coins in the sets (1n, 2d, 2q) containing 1 nickel, 2 dimes and 2 quarters in each set.

The worth of each set is 5+2*10+2*25 = 75 cents.

The number of these groups is  =  = 8.

Thus there are 8 nickels, 16 dimes, and 16 quarters among remained coins.

So, the answer is:  8 nickels, 16+1 = 17 dimes, and 16 quarters in the original collection.


Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
Harry has $6.10 in his pocket.
$0.25Q + $0.10D + $0.05N = $6.10

or multiplying through by 100,

25Q + 10D + 5N = 610

dividing through by 5

5Q + 2D + N = 122

He has twice as many quarters as nickels
Q = 2N

and
one more dime than quarters. 
D = Q + 1

So we have this system of equations:

1.     5Q + 2D + N = 122
2.               Q = 2N
3.               D = Q + 1

Use eq. 2 to substitute 2N for Q in eq. 3

3.               D = Q + 1
4.               D = 2N + 1

Use eq. 2 to substitute 2N for Q in eq. 1 and
use eq. 4 to substitute 2N + 1 for D in eq 1:

1.               5Q + 2D + N = 122
       5(2N) + 2(2N + 1) + N = 122 
            10N + 4N + 2 + N = 122
                     15N + 2 = 122
                         15N = 120
                           N = 8

Substitute 8 for N in eq. 4:

4.               D = 2N + 1
                 D = 2(8) + 1
                 D = 16 + 1
                 D = 17


Substitute N=8 in eq. 2

2.               Q = 2N
                 Q = 2(8)
                 Q = 16

Edwin
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