Mary has $3.00 in nickels, dimes, and quarters. if she has twice as many dimes as quarters and twenty-seven more nickels than dimes, how many coins of each type does she have?

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Let q = number of quarters
then from "she has twice as many dimes as quarters"
2q = number of dimes
and from "five more nickels than dimes"
2q+5 = number of nickels
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Since she has a total of $3.00:
.25q + .10(2q) + .05(2q+5) = 3.00
.25q + .20q + .10q + .25 = 3.00
.55q + .25 = 3.00
.55q = 2.75
q = 2.75/.55
q = 5 (number of quarters)
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number of dimes:
2q = 2(5) = 10 (number of dimes)
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number of nickels:
2q+5 = 2(5)+5 = 10 + 5 = 15 (number of nickels)