SOLUTION: Alex has four times as many quarters as nickels and five more dimes than nickels in his coin bank. If he has $12.00 in nickels, dimes and quarters in the coin bank, how many of ea

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Question 1055022: Alex has four times as many quarters as nickels and five more dimes than nickels in his coin bank. If he has $12.00 in nickels, dimes and quarters in the coin bank, how many of each coin does he have ?
Found 2 solutions by addingup, ikleyn:
Answer by addingup(3677)   (Show Source): You can put this solution on YOUR website!
q = 4n
d = n+5
-------------------
0.05n+0.10d+0.25q = 12 substitute for d and q
0.05n+0.10(n+5)+0.25(4n) = 12
0.05n+0.10n+0.50+1n = 12
1.15n = 11.50
n = 10 he has 10 nickels
And:
q = 4n = 10(4) = 40 quarters
d = n+5 = 10+5 = 15 dimes
-------------------
Check:
10n = 0.05*10 = 0.50
15d = 0.10*15 = 1.50
40q = 0.25*40 = 10
Total . . . . . 12.00 Correct
Answer by ikleyn(52756)   (Show Source): You can put this solution on YOUR website!
.
Alex has four times as many quarters as nickels and five more dimes than nickels in his coin bank.
If he has $12.00 in nickels, dimes and quarters in the coin bank, how many of each coin does he have ?
~~~~~~~~~~~~~~~~~~~~~~~~ 

For a moment, take off 5 dimes from the collection (mentally).
The value of the remaining coins in the collection will be
1150 cents.

Then the number of quarters is four times the number of nickels 
and  the number of (remaining) dimes is equal to the number of nickels.

It means that you can group the remaining coins in the sets each consisting of 
1 nickel, 1 dime and 4 quarters. 
Each such set worth is 4*25+10+5 = 115 cents. 

How much such sets are there among the remaining coins?
But of course,  = 10.

Having this, you can easily complete the solution ( ! Mentally !)


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