document.write( "Question 1098751: A parking meter contains quarters and dimes worth ​$12.80. There are 77 coins in all. Find how many of each there are? \n" ); document.write( "
Algebra.Com's Answer #713150 by ikleyn(52777)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "        There are different methods to solve the problem.
\n" ); document.write( "        I will show you 3 (three) basic methods in this post.\r
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\n" ); document.write( "\n" ); document.write( "1- Algebra solution,   2 equations approach\r
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document.write( "Let d be the number of dimes and q be the number of quarters.\r\n" );
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document.write( "Then you have this system of two equations\r\n" );
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document.write( "  d +   q =   77,        (1)    (counting dimes)\r\n" );
document.write( "10d + 25q = 1280.        (2)    (counting cents)\r\n" );
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document.write( "To solve it, multiply eq(1) by 10. You will have\r\n" );
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document.write( "10d + 10q =  770,        (1')\r\n" );
document.write( "10d + 25q = 1280.        (2')\r\n" );
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document.write( "Next subtract (1') from (2'). You will get\r\n" );
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document.write( "25q - 10q = 1280 - 770,\r\n" );
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document.write( "15q = 510  ====>  q = \"510%2F15\" = 34.\r\n" );
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document.write( "The parking meter contains 34 quarters and 77-34 = 43 dimes.\r\n" );
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document.write( "Check.   43*10 + 34*25 = 33*10 + 34*25 = 1280.    !  Correct !\r\n" );
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document.write( "Answer.  34 quarters and 43 dimes.\r\n" );
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\n" ); document.write( "\n" ); document.write( "2- Algebra solution,   1 equation approach\r
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document.write( "Let  q be the number of quarters.\r\n" );
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document.write( "Then the number of dimes is (77-q). \r\n" );
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document.write( "The quarters contribute 25q cents toward the total.\r\n" );
document.write( "The dimes contribut 10*(77-q) toward the total.\r\n" );
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document.write( "The total is  25q + 10*(77-q).\r\n" );
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document.write( "From the other side, it is 1280 cents, according to the condition.\r\n" );
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document.write( "It gives you an equation\r\n" );
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document.write( "25q + 10*(77-q) = 1280.     \r\n" );
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document.write( "Simplify and solve for q:\r\n" );
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document.write( "25q + 770 - 10q = 1280 \r\n" );
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document.write( "15q = 1280 - 770  \r\n" );
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document.write( "15q = 510  ====>  q = \"510%2F15\" = 34.\r\n" );
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document.write( "The parking meter contains 34 quarters and 77-34 = 43 dimes.\r\n" );
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document.write( "You got the same answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "2- Logical analysis (MENTAL solution without using equations)\r
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document.write( "Imagine for a minute that all coins in the parking meter are DIMES.\r\n" );
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document.write( "Then you would have 10*77 = 770 cents in the parking meter.\r\n" );
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document.write( "But in reality the money amount there is 1280 cents, which is 1280-770 = 510 cents more than 770 cents.\r\n" );
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document.write( "Why we have this difference ?  - But of course, because we counted 25-cent quarters as 10-cent coins.\r\n" );
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document.write( "Then it is clear, that the number of quarters is  \"510%2F%2825-10%29\" = \"510%2F15\" = 30 + 4 = 34.\r\n" );
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document.write( "And you get the same answer.\r\n" );
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\n" ); document.write( "Congratulations !   You are now familiar with 3 basic methods for solving typical coin problems.\r
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\n" ); document.write( "\n" ); document.write( "I suggest that algebraic methods will be your basic methods for such problems,\r
\n" ); document.write( "\n" ); document.write( "and the logical analysis method will allow you to solve the problems MENTALLY without using equations.\r
\n" ); document.write( "\n" ); document.write( "I will be happy if it will make your horizon wider.\r
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\n" ); document.write( "To see other similar solved coin problems, look in the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Coin problems\r
\n" ); document.write( "\n" ); document.write( "    - More Coin problems\r
\n" ); document.write( "\n" ); document.write( "    - Solving coin problems without using equations\r
\n" ); document.write( "\n" ); document.write( "    - Typical coin problems from the archive\r
\n" ); document.write( "\n" ); document.write( "    - Solving coin problems mentally by grouping without using equations\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "To see how the logical method works for other similar problems, look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Problem on two-wheel and three-wheel bicycles\r
\n" ); document.write( "\n" ); document.write( "    - Problem on animals at a farm\r
\n" ); document.write( "\n" ); document.write( "    - Problem on pills in containers\r
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