document.write( "Question 99334: Sharon has 25 poins. They are all quarters and nickels. She has a total of $2.85. How many quarters and nickels does she have? Construct an algebraic equation, solve for the varriable, and answer the question. \n" ); document.write( "
Algebra.Com's Answer #72267 by bucky(2189)\"\" \"About 
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The problem tells you two things ... first it tells you that the number of quarters
\n" ); document.write( "(call that Q) plus the number of nickels (call that N) adds up to be 25. In equation form
\n" ); document.write( "this can be written as:
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\n" ); document.write( "Q + N = 25
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\n" ); document.write( "Next the problem tells you that the total value of the coins is $2.85 or 285 cents.
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\n" ); document.write( "Since each quarter is 25 cents, the number of quarters (Q) times 25 is the number of cents
\n" ); document.write( "from quarters. And since each nickel is 5 cents, the number of nickels (N) times 5 is the number
\n" ); document.write( "of cents from nickels. These two must add to be 285. In equation form this is:
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\n" ); document.write( "25Q + 5N = 285
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\n" ); document.write( "Returning to the first equation, you can subtract N from both sides to get:
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\n" ); document.write( "Q = 25 - N
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\n" ); document.write( "which simply says that if you subtract the number of nickels from 25 total coins, you
\n" ); document.write( "are left with the number of quarters. Since Q = 25 - N you can replace Q by 25 - N in the
\n" ); document.write( "second equation that involves the total value of the coins. Substituting 25 - N for Q
\n" ); document.write( "results in this equation becoming:
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\n" ); document.write( "25(25 - N) + 5N = 285
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\n" ); document.write( "Do the distributed multiplication on the left side by multiplying 25 times each of the terms
\n" ); document.write( "in the parentheses to make the equation become:
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\n" ); document.write( "625 - 25N + 5N = 285
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\n" ); document.write( "Combine the two terms on the left side that involve N and the equation then becomes:
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\n" ); document.write( "625 - 20N = 285
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\n" ); document.write( "Next get rid of the 625 on the left side by subtracting 625 from both sides to reduce the
\n" ); document.write( "equation to:
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\n" ); document.write( "-20N = -340
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\n" ); document.write( "Finally, solve for N by dividing both sides by -20 ... the multiplier of N ... to get:
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\n" ); document.write( "N = -340/-20 = 340/20 = 17
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\n" ); document.write( "This tells us that there are 17 nickels and since the total number of coins is 25, the
\n" ); document.write( "remaining 8 coins must be quarters. So the answer is 17 nickels and 8 quarters.
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\n" ); document.write( "Check ... The first condition of the problem is that the number of coins is 25, and that
\n" ); document.write( "is met because 17 + 8 = 25.
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\n" ); document.write( "The second condition is that the amount of money must be $2.85. Well, 8 quarters is equivalent
\n" ); document.write( "to $2.00 and 17 nickels at 5 cents each is (17*5) 85 cents. So the total value of the
\n" ); document.write( "coins is $2.00 + 0.85 = $2.85.
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\n" ); document.write( "The answer checks on both accounts.
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\n" ); document.write( "Hope this helps you to understand the problem and how to solve it.
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