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Question 515927: I am having trouble figuring out how to deal with the Ned to figure out the 21 coins part of this problem. I can get X=11 but after that I am lost. Here is the problem
Mrs Lynch has 21 coins in nickels and dimes The total value is 1.65 how many of each coin does she have?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let's work this problem in pennies. Each nickel is 5 pennies and each dime is 10 pennies. The value of Mrs. Lynch's coins is $1.65 which is 165 pennies.
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Let N represent the unknown number of nickels and D represent the unknown number of dimes.
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We know two facts that can be written as equations so that we can solve this problem. The first fact is that if we add the number of nickels (N) to the number of dimes (D) the total will be 21. So we can write in equation form that nickels plus dimes equals 21, or:
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N + D = 21
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The second fact is that if we multiply the number of nickels (N) by 5 pennies per nickel, we get the number of pennies because of the nickels. Also if we multiply the number of dimes (D) by 10 pennies per dime, we get the number of pennies because of the dimes. Then if we total these two we get the total number of pennies which we know is 165. In equation form this is:
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5N + 10D = 165
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One of the ways we can solve this pair of equations is by substitution. Return to the first equation and let's rearrange it by subtracting D from both sides. When you do that subtraction, the D disappears on the left side and a -D appears on the right side as follows:
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N = 21 - D
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Now we can go to the second equation and in it replace the N by 21 - D which is equal to N. With this substitution the second equation becomes:
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5(21 - D) + 10D = 165
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Multiply the 5 times each of the terms in parentheses and you get:
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105 - 5D + 10D = 165
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Combine the - 5D and the + 10D and you get:
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105 + 5D = 165
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Get rid of the 105 on the left side by subtracting 105 from both sides and you are left with:
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5D = 60
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Solve for D, the number of dimes, by dividing both sides by 5 and you have:
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D = 12
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This tells us that Mrs Lynch has 12 dimes. Since the total number of coins is 21, we subtract 12 from 21 and find that the number of nickels is 9.
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Let's check our answer. 12 dimes is a dollar and 20 cents. and 9 nickels is 45 cents. When you add these two together you get $1.65, just as it is supposed to be. Therefore, our answer is correct ... 12 dimes and 9 nickels.
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Hope this helps you to understand the problem.
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