SOLUTION: a jar contains 40 coins consisting of dimes and quarters and having a total value of $4.90. how many of each kind of coin are there?: a jar contains 40 coins consisting of dimes an

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Question 51636: a jar contains 40 coins consisting of dimes and quarters and having a total value of $4.90. how many of each kind of coin are there?: a jar contains 40 coins consisting of dimes and quarters and having a total value of $4.90. how many of each kind of coin are there?
Answer by rchill(405) About Me  (Show Source):
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We have two equations: q%2Bd=40 represents the number of q quarters and d dimes, and .25q%2B.10d=4.90 represents the total value of the 40 coins. Solving for d in the first equation yields d=40-q and we substitute that into the second equation for d: .25q%2B.10%2A%2840-q%29=4.90. Expanding this latest equation produces .25q%2B4-.10q=4.90. Now combine like terms: .15q%2B4=4.90. Subtracting 4 from each side produces: .15q=.90. And now divide both sides by .15 yields q=6. That means there are 6 quarters. Because we know there are 40 coins total, there must be 40-6, or 34, dimes. To verify that answer, 34 dimes is $3.40 and 6 quarters is $1.50. Adding those two values together produces $4.90, which means our answer of 6 quarters and 34 dimes is correct.