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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.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The problem tells you two things ... first it tells you that the number of quarters
(call that Q) plus the number of nickels (call that N) adds up to be 25. In equation form
this can be written as:
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Q + N = 25
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Next the problem tells you that the total value of the coins is $2.85 or 285 cents.
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Since each quarter is 25 cents, the number of quarters (Q) times 25 is the number of cents
from quarters. And since each nickel is 5 cents, the number of nickels (N) times 5 is the number
of cents from nickels. These two must add to be 285. In equation form this is:
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25Q + 5N = 285
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Returning to the first equation, you can subtract N from both sides to get:
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Q = 25 - N
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which simply says that if you subtract the number of nickels from 25 total coins, you
are left with the number of quarters. Since Q = 25 - N you can replace Q by 25 - N in the
second equation that involves the total value of the coins. Substituting 25 - N for Q
results in this equation becoming:
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25(25 - N) + 5N = 285
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Do the distributed multiplication on the left side by multiplying 25 times each of the terms
in the parentheses to make the equation become:
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625 - 25N + 5N = 285
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Combine the two terms on the left side that involve N and the equation then becomes:
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625 - 20N = 285
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Next get rid of the 625 on the left side by subtracting 625 from both sides to reduce the
equation to:
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-20N = -340
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Finally, solve for N by dividing both sides by -20 ... the multiplier of N ... to get:
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N = -340/-20 = 340/20 = 17
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This tells us that there are 17 nickels and since the total number of coins is 25, the
remaining 8 coins must be quarters. So the answer is 17 nickels and 8 quarters.
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Check ... The first condition of the problem is that the number of coins is 25, and that
is met because 17 + 8 = 25.
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The second condition is that the amount of money must be $2.85. Well, 8 quarters is equivalent
to $2.00 and 17 nickels at 5 cents each is (17*5) 85 cents. So the total value of the
coins is $2.00 + 0.85 = $2.85.
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The answer checks on both accounts.
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Hope this helps you to understand the problem and how to solve it.
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