Question 1162245
<br>
Take the time to set up the problem using a single variable.  Blindly plunging into solving the problem using three variables will make more work for you.<br>
The given information compares nickels to dimes and quarters to nickels.  That is a clue that almost certainly it will be easiest to set up the problem using the number of nickels as the variable.<br>
x = number of nickels
x-4 = number of dimes  [the number of nickels is 4 more than the number of dimes]
2x = number of quarters  [there are twice as many quarters as nickels]<br>
The total value is $6.10, or 610 cents:<br>
{{{25(2x)+10(x-4)+5(x) = 610}}}<br>
{{{50x+10x-40+5x = 610}}}
{{{65x = 650}}}
{{{x = 10}}}<br>
ANSWER:
nickels: x = 10
dimes: x-4 = 6
quarters: 2x = 20<br>
CHECK:
10(5)+6(10)+20(25) = 50+60+500 = 610<br>
Solving problems like this using mental arithmetic and logical reasoning can be good mental exercise.  It might go something like this:<br>
Loan Kelly 4 more dimes, so that the numbers of nickels and dimes are the same.  The total value is now 610+40 = 650.<br>
The coins now consist of a number of nickels, an equal number of dimes, and twice that many quarters.  A group of one nickel, one dime, and two quarters together has a value of 65 cents.<br>
Since the new total value of the coins is 650 cents, that must mean there are 10 of those groups -- making 10 nickels, 10 dimes, and 20 quarters.<br>
Now have Kelly give you back the 4 dimes you loaned her, to find that the coins she has are 10 nickels, 6 dimes, and 20 quarters.<br>