SOLUTION: A collection of nickels, dimes and quarters is worth $5.30. There are two more dimes than nickels and four more quarters than dimes. How many quarters are in the collection of co

Question 1007081: A collection of nickels, dimes and quarters is worth $5.30. There are two more dimes than nickels and four more quarters than dimes. How many quarters are in the collection of coins?
Answer by ikleyn(52767) (Show Source): You can put this solution on YOUR website!
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A collection of nickels, dimes and quarters is worth $5.30. There are two more dimes than nickels and four more quarters than dimes. How many quarters are in the collection of coins?
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Mathematical model is

5n + 10d + 25q = 530,
d = n + 2,
q = d + 4.

Express n via d from the second equation: n = d - 2, and then substitute it into the first equation.
Also, substitute q from the third equation into the first one. You will get 

5(d-2) + 10d +25(d+4) = 530.

Simplify it:

5d + 10d + 25d = 530 + 5*2 - 25*4, or

40d = 440.

Hence, d =  = 11.

Now define yourself the remaining unknowns n and q.

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