SOLUTION: Katie has a collection of nickels, dimes and quarters with a total value of $6.80. There are 5 more dimes than nickels and 6 more quarters than nickels, how many of each coin does

Algebra.Com
Question 1205719: Katie has a collection of nickels, dimes and quarters with a total value of $6.80. There are 5 more dimes than nickels and 6 more quarters than nickels, how many of each coin does she have?
Found 4 solutions by ikleyn, josgarithmetic, greenestamps, MathTherapy:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Katie has a collection of nickels, dimes and quarters with a total value of $6.80.
There are 5 more dimes than nickels and 6 more quarters than nickels, how many of each coin does she have?
~~~~~~~~~~~~~~~~~~~~~~ 

Let x be the number of nickels;

then the number of dimes is (x+5) and the number of quarters is (x+6).


Write the total money equation in cents

    5x + 10*(x+5) + 25*(x+6) = 680 cents.


Simplify and find x

    5x + 10x + 50 + 25x + 150 = 680

    5x + 10x + 25x = 680 - 50 - 150

         40x       =      480

           x       =      480/40 = 12.


ANSWER.  There are 12 nickels,  12+5 = 17 dimes  and  12+6 = 18 quarters.


CHECK.   12*5 + 17*10 + 18*25 = 680 cents, total.    ! correct !

Solved.



Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
n, how many nickels
n+5, how many dimes
n+6, how many quarters

Total value of $6.80 means .
Simplify and solve.
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


You can solve the problem informally, using steps that are nearly the same as the formal algebraic solution shown by the other tutor.

Probably this problem was supposed to be solved using formal algebra; but you can get good mental exercise solving the problem without it.

The value of the 5 "extra" dimes is 5($0.10) = $0.50; the value of the 6 "extra" quarters is 6($0.25) = $1.50. The total value of those "extra" coins is $0.50 $1.50 = $2.00.

So the value of the remaining coins is $6.80 - $2.00 = $4.80.

Those coins are equal numbers of nickels, dimes, and quarters. The total value of a group consisting of one nickel, one dime, and one quarter is $0.40. To make the remaining $4.80, the number of those groups must be $4.80/$0.40 = 12.

So the number of nickels is 12; the number of dimes is 12+5 = 17, and the number of quarters is 12+6 = 18.

ANSWERS: 12 nickels, 17 dimes, 18 quarters
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Katie has a collection of nickels, dimes and quarters with a total value of $6.80. There are 5 more dimes than nickels and 6 more quarters than nickels, how many of each coin does she have?

Let number of nickels be N
Then, number of dimes and quarters = N + 5, and N + 6, respectively

Value of nickels: .05N
Value of dimes:    .1(N + 5) = .1N + .5
Value of quarters:.25(N + 6) = .25N + 1.5 

As total value is 6.80, we get:  .05N + .1N + .5 + .25N + 1.5 = 6.8
                                                      .4N + 2 = 6.8
                                                          .4N = 4.8
                                     Number of nickels, or  

Now, calculate number of dimes (N + 5), and number of quarters (N + 6).
RELATED QUESTIONS

Katie has a collection of nickels, dimes, and quarters with a total value of $4.95. There (answered by richwmiller)
Katie has a collection of nickels, dimes and quarters with a total value of $4.30. There... (answered by rothauserc)
Katie has a collection of nickels, dimes and quarters with a total value of $3.75. There... (answered by josgarithmetic,MathTherapy)
Katie has a collection of nickels, dimes and quarters with a total value of $6.10 . There (answered by stanbon)
Katie has a collection of nickels, dimes and quarters with a total value of $4.25.There (answered by josgarithmetic)
Katie has a collection of nickels, dimes, and quarters with a total value of $4.65. There (answered by math_helper)
Katie has a collection of nickels, dimes and quarters with a total value of $4.85.... (answered by ikleyn)
Katie has a collection of nickels, dimes and quarters with a total value of $5.45. There... (answered by ikleyn)
Katie has a collection of nickels, dimes and quarters with a total value of $8.15. There... (answered by TimothyLamb)