SOLUTION: Kelly has a collection of nickels, dimes, and quarters with a total value of $6.10. There are four more nickels than dimes and twice as many quarters as nickels. How many of each c

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Question 1162245: Kelly has a collection of nickels, dimes, and quarters with a total value of $6.10. There are four more nickels than dimes and twice as many quarters as nickels. How many of each coin is in her collection?
Found 3 solutions by Theo, greenestamps, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
n = number of nickels, d = number of dimes, q = number of quarters.
the value of a nickel is.05, the balue of a dime is .1, the value of a quarter is .25
.05 * n + .1 * d + .25 * q = 6.10
n = d + 4
q = 2 * n
you want to make all values in terms of nickels.
from n = d + 4, you get d = n - 4
you already have q = 2 * n
the equation of .05 * n + .1 * d + .25 * q = 6.10 becomes:
.05 * n + .1 * (n - 4) + .25 * (2 * n) = 6.10
simplify to get:
.05 * n + .1 * n - .4 + .5 * n = 6.10
combine like terms to get:
.65 * n - .4 = 6.10
add .4 to both sides of the equation to get:
.65 * n = 6.5
solve for n to get:
n = 10
since d = n - 4, then d = 6
since q = 2 * n, then q = 20
you have 10 nickels, 6 dimes, and 20 quarters.
their total value is 10 * .05 + 6 * .1 + 20 * .25 = 6.10.
10 nickels, 6 dimes, and 20 quarters is your solution.
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


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.

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.

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]

The total value is $6.10, or 610 cents:







ANSWER:
nickels: x = 10
dimes: x-4 = 6
quarters: 2x = 20

CHECK:
10(5)+6(10)+20(25) = 50+60+500 = 610

Solving problems like this using mental arithmetic and logical reasoning can be good mental exercise. It might go something like this:

Loan Kelly 4 more dimes, so that the numbers of nickels and dimes are the same. The total value is now 610+40 = 650.

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.

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.

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.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Kelly has a collection of nickels, dimes, and quarters with a total value of $6.10. There are four more nickels than dimes and twice as many quarters as nickels. How many of each coin is in her collection?
Let the number of nickels be N

Then number of dimes = N - 4, and number of quarters: 2N

We then get: .05N + .1(N - 4) + .25(2N) = 6.1

.05N + .1N - .4 + .5N = 6.1

.65N = 6.1 + .4

.65N = 6.5

Number of nickels, or 

You should now be able to find the number of dimes, and quarters. 

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