SOLUTION: Katie has a collection of nickels, dimes and quarters with a total value of $6.70. There are 3 more dimes than nickels and 8 more quarters than nickels, how many of each coin d

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Question 1046549: Katie has a collection of nickels, dimes and quarters with a total value of
$6.70. There are 3 more dimes than nickels and 8
more quarters than nickels, how many of each coin does she have?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39623)   (Show Source): You can put this solution on YOUR website!


Multiply the money count equation by 20.


Find two convenient substitutions to do, and first solve for n using the money count equation.
Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

Katie has a collection of nickels, dimes and quarters with a total value of
$6.70. There are 3 more dimes than nickels and 8
more quarters than nickels, how many of each coin does she have?
Let number of nickels, dimes, and quarters, be N, D, and Q, respectively

Then, .05N + .1D + .25Q = 6.7 ------- eq (i)

Also, D = N + 3 ------ eq (ii)

And, Q = N + 8 ------- eq (iii)

.05N + .1(N + 3) + .25(N + 8) = 6.7 ------- Substituting N + 3 for D, and N + 8 for Q in eq (i)

.05N + .1N + .3 + .25N + 2 = 6.7

.4N + 2.3 = 6.7

.4N = 6.7 - 2.3

.4N = 4.4

N, or number of nickels = , or 

Number of dimes: 11 + 3, or 

Number of quarters: 11 + 8, or  

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