A collection of 30 coins worth $5.50 consists of nickels, dimes, and quarters. There are twice as many dimes as nickels. How many quarters are there?

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A collection of 30 coins worth $5.50 consists of nickels, dimes, and quarters. There are twice as many dimes as nickels. How many quarters are there?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Q + D + N = 30 there are more dimes than nickels D=2N $5.50 = 550 cents each Q is worth 25 cents, D 10 cents, N 5 cents -> 25Q+10D+5N = 550 solve using substitution sub 2N for D in top equation Q +2N +N = 30 Q+3N = 30 3N = 30-Q N = 10-(1/3)Q sub this in for N ->25Q +10(2*(10-(1/3)Q))+5(10-(1/3)Q) = 550 distribute and add like terms (50/3)Q +250 = 550 Q = (550-250)*(3/50) Q = 90/5 = 18
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