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
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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(52765) (Show Source):
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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.
