document.write( "Question 1100231: a jar contains half dollars and qouarters there are 30 coins in all in the jar the total value of coins is $8.75 how many half dollars there is in the jar
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Algebra.Com's Answer #714717 by ikleyn(52803) $\"\"$ $\"About$

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document.write( "  Q +  H =   30     (1)   (counting coins)    Q stands for quarters\r\n" );
document.write( "25Q + 50H = 875     (2)   (counting cents)    H stands for half-dollars\r\n" );
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document.write( "In eq(2) cancel the factor 25 in both sides. You will get the modified system in the form\r\n" );
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document.write( "  Q +  H =   30     (1')\r\n" );
document.write( "  Q +  2H =  35     (2')\r\n" );
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document.write( "Next subtract eq(1') from eq(2') (both sides).  You will get\r\n" );
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document.write( "       H = 35 - 30 = 5.\r\n" );
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document.write( "Answer.  5  half-dollars and 30-5 = 25 quarters.\r\n" );
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\n" ); document.write( "\n" ); document.write( "2. Logical analysis (MENTAL solution; no equation/equations required)\r
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document.write( "Let assume for a minute that all 30 coins are 25-cent quarters.\r\n" );
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document.write( "Then the total would be 30*25 = 750 cents.\r\n" );
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document.write( "But in reality we have 875 cents.\r\n" );
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document.write( "It because we counted half-dollars as quarters.\r\n" );
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document.write( "Now, let start return back these half-dollars.\r\n" );
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document.write( "With each returned half-dollar we diminish the difference of 875-750 = 125 cents by 25 cents.\r\n" );
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document.write( "How many half-dollars should we return ? - But of course,  = 5 half-dollars.\r\n" );
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document.write( "We completed our calculations and got the same answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "And returned back all half-dollars.\r
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\n" ); document.write( "On coin problems see 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( "    - Kevin and Randy Muise have a jar containing coins\r
\n" ); document.write( "\n" ); document.write( "    - Typical coin problems from the archive\r
\n" ); document.write( "\n" ); document.write( "    - Three methods for solving standard (typical) coin word problems\r
\n" ); document.write( "\n" ); document.write( "    - More complicated coin problems\r
\n" ); document.write( "\n" ); document.write( "    - Solving coin problems mentally by grouping without using equations\r
\n" ); document.write( "\n" ); document.write( "    - Santa Claus helps solving coin problem\r
\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on coin word problems\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "You will find there the lessons for all levels - from introductory to advanced,
\n" ); document.write( "and for all methods used - from one equation to two equations and even without equations. \r
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\n" ); document.write( "\n" ); document.write( "Read them and become an expert in solution of coin problems.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Coin problems\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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