Question 95751This question is from textbook
: Carol has 18 coins with a total value of $3.45. If the coins are dimes and quaters, how many of each kind are there?
This question is from textbook
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let D represent the number of dimes and Q represent the number of quarters.
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Since you are told that the number of coins is 18, you can add the number of dimes (D) to
the number of quarters (Q) and set that sum equal to 18. In equation form this is:
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D + Q = 18 <=== call this "equation 1"
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The total amount of the coins is $3.45 or 345 cents. Each dime is 10 cents and each quarter
is 25 cents. Therefore, if you multiply the number of dimes (D) times 10 (the number of
cents per dime), you will get the total number of cents for all the dimes. Similarly, if
you multiply the number of quarters (Q) times 25 (the number of cents per quarter), you
will get the total number of cents for all the quarters. And when you add the total
cents for dimes to the total cents for quarters, the sum is to be 345 cents. In equation
form this is:
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10D + 25Q = 345 <=== call this "equation 2"
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Now you can return to equation 1 and solve it for either D or Q. Suppose you solve it
for D by subtracting Q from each side of the equation. When you do that you get:
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D = 18 - Q
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Now return to equation 2 and since D is equal to 18 - Q you can substitute 18 - Q for D
in equation 2. When you do that equation 2 becomes:
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10(18 - Q) + 25Q = 345
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Do the multiplication of each of the two terms in parentheses by the 10 and the equation becomes:
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180 - 10Q + 25Q = 345
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Get rid of the 180 on the left side by subtracting 180 from both sides. When you do that
the equation is reduced to:
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-10Q + 25Q = 165
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On the left side combine the -10Q and the +25Q to get +15Q:
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15Q = 165
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Finally, solve for Q by dividing both sides by 15 to get:
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Q = 165/15 = 11
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This says that you have 11 quarters and since you know there are 18 coins, the remaining
7 coins must be the number of dimes.
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Check by determining that 11 quarters at 25 cents per quarter is $2.75 and then determining
that 7 dimes is $0.70. The total of $2.75 and $0.70 is $3.45 just as the problem said it was.
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Therefore, the answer to this problem is 11 quarters and 7 dimes.
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Hope this helps you to understand the problem and a way to go about solving it.
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