Mia H.

asked • 11/02/14

Money Denomination Problem

Witny Librun has a collection of pennies, dimes, and quarters, the number of dimes is one less than twice the number of pennies. if there are 27 coins in all worth a total of $4.20 how mnay of each denomination of coin is in the collection. 

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DI Z. answered • 11/02/14

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Suppose WL has P pennies, D dimes and Q quarters, D=2P-1, D+P+Q=27, 10D+P+25Q=420
Solve for P, P=5, then D=9, thus Q=13.
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Mia H.

so how would i solve for each letter?
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11/02/14

DI Z.

D+P+Q=27, both sides multiple by 25, you have 25D+25P+25Q=25*27=675, you have another equation, 10D+P+25Q=420, use the previous equation minus this one, you get 15D+24P=255. Remember you have another D=2P-1, then multiple by 15, you get 15D=30P-15, thus, 30P-15+24P=255, 54P=270, P=5. Then, D=2P-1=9, Q=13.
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11/02/14

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