document.write( "Question 95751This question is from textbook
\n" ); document.write( ": 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? \n" ); document.write( "
Algebra.Com's Answer #69773 by bucky(2189)\"\" \"About 
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Let D represent the number of dimes and Q represent the number of quarters.
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\n" ); document.write( "Since you are told that the number of coins is 18, you can add the number of dimes (D) to
\n" ); document.write( "the number of quarters (Q) and set that sum equal to 18. In equation form this is:
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\n" ); document.write( "D + Q = 18 <=== call this \"equation 1\"
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\n" ); document.write( "The total amount of the coins is $3.45 or 345 cents. Each dime is 10 cents and each quarter
\n" ); document.write( "is 25 cents. Therefore, if you multiply the number of dimes (D) times 10 (the number of
\n" ); document.write( "cents per dime), you will get the total number of cents for all the dimes. Similarly, if
\n" ); document.write( "you multiply the number of quarters (Q) times 25 (the number of cents per quarter), you
\n" ); document.write( "will get the total number of cents for all the quarters. And when you add the total
\n" ); document.write( "cents for dimes to the total cents for quarters, the sum is to be 345 cents. In equation
\n" ); document.write( "form this is:
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\n" ); document.write( "10D + 25Q = 345 <=== call this \"equation 2\"
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\n" ); document.write( "Now you can return to equation 1 and solve it for either D or Q. Suppose you solve it
\n" ); document.write( "for D by subtracting Q from each side of the equation. When you do that you get:
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\n" ); document.write( "D = 18 - Q
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\n" ); document.write( "Now return to equation 2 and since D is equal to 18 - Q you can substitute 18 - Q for D
\n" ); document.write( "in equation 2. When you do that equation 2 becomes:
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\n" ); document.write( "10(18 - Q) + 25Q = 345
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\n" ); document.write( "Do the multiplication of each of the two terms in parentheses by the 10 and the equation becomes:
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\n" ); document.write( "180 - 10Q + 25Q = 345
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\n" ); document.write( "Get rid of the 180 on the left side by subtracting 180 from both sides. When you do that
\n" ); document.write( "the equation is reduced to:
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\n" ); document.write( "-10Q + 25Q = 165
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\n" ); document.write( "On the left side combine the -10Q and the +25Q to get +15Q:
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\n" ); document.write( "15Q = 165
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\n" ); document.write( "Finally, solve for Q by dividing both sides by 15 to get:
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\n" ); document.write( "Q = 165/15 = 11
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\n" ); document.write( "This says that you have 11 quarters and since you know there are 18 coins, the remaining
\n" ); document.write( "7 coins must be the number of dimes.
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\n" ); document.write( "Check by determining that 11 quarters at 25 cents per quarter is $2.75 and then determining
\n" ); document.write( "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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\n" ); document.write( "Therefore, the answer to this problem is 11 quarters and 7 dimes.
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\n" ); document.write( "Hope this helps you to understand the problem and a way to go about solving it.
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