document.write( "Question 176804: 1. Nine years ago,the sum of Carlo's age and Ronald's is greater than 28.
\n" ); document.write( " Carlo is 6 years older than Ronald. How old is Ronald now?\r
\n" ); document.write( "\n" ); document.write( "2. Group the pairs of terms having a common monomial factor.\r
\n" ); document.write( "\n" ); document.write( " $\"15x%5E2%2B27y%5E2%2B16x%5E2-12x%2B15c%5E2-15cd%2B20r%5E2-45r-18b%5E3-30b%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( "3. Determine the common monomial factors. \n" ); document.write( "

Algebra.Com's Answer #131927 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
1. Nine years ago,the sum of Carlo's age and Ronald's is greater than 28.
\n" ); document.write( " Carlo is 6 years older than Ronald. How old is Ronald now?
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document.write( "R = Ronald's age now.\r\n" );
document.write( "C = Carlo's age now.\r\n" );
document.write( "R-9 = Ronald's age 9 years ago\r\n" );
document.write( "C-9 = Carlo's age 9 years ago.\r\n" );
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\n" ); document.write( ">>...nine years ago,the sum of Carlo's age, C-9, and Ronald's, R-9, is greater than 28...<<\r
\n" ); document.write( "\n" ); document.write( " $\"%28C-9%29+%2B+%28R-9%29+%3E+28\"$ \r
\n" ); document.write( "\n" ); document.write( "that simplifies to:\r
\n" ); document.write( "\n" ); document.write( " $\"C-9+%2B+R-9+%3E+28\"$
\n" ); document.write( " $\"C+-+18+%3E+28\"$
\n" ); document.write( " $\"C+%3E+46\"$
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\n" ); document.write( ">>...Carlo is 6 years older than Ronald...<<
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document.write( "C = R + 6\r\n" );
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document.write( "Substitute R + 6 for C in:\r\n" );
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document.write( "            C > 46\r\n" );
document.write( "        R + 6 > 46\r\n" );
document.write( "            R > 40\r\n" );
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document.write( "So thare are many possibilities:\r\n" );
document.write( "Ronald is 41 and Carlos is 47\r\n" );
document.write( "Ronald is 42 and Carlos is 48\r\n" );
document.write( "Ronald is 43 and Carlos is 49\r\n" );
document.write( "Ronald is 44 and Carlos is 50\r\n" );
document.write( "Ronald is 45 and Carlos is 51\r\n" );
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document.write( "until the ages get so large that \r\n" );
document.write( "nobody lives to be that old.\r\n" );
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document.write( "So there is not just one answer. Did you leave \r\n" );
document.write( "something out?\r\n" );
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\n" ); document.write( "2. Group the pairs of terms having a common monomial factor. \r
\n" ); document.write( "\n" ); document.write( " $\"15x%5E2%2B27y%5E2%2B16x%5E2-12x%2B15c%5E2-15cd%2B20r%5E2-45r-18b%5E3-30b%5E2\"$
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document.write( "The first two terms have a common monomial factor of 3.  Since both those terms\r\n" );
document.write( "are positive, we just group them with a set of parentheses:\r\n" );
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document.write( "The next two terms have a common monomial factor of 4x.  Since both those terms\r\n" );
document.write( "are positive, we just group them with a set of parentheses as before:\r\n" );
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document.write( "The next two terms have a common monomial factor of 5c.  Since both those terms\r\n" );
document.write( "are positive, we just group them with a set of parentheses as before:\r\n" );
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document.write( "The next two terms have a common monomial factor of 5r.  Since both those terms\r\n" );
document.write( "are positive, we just group them with a set of parentheses as before:\r\n" );
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document.write( "Now we have to watch it because the first of the last two terms is a\r\n" );
document.write( "negative. In that case we insert not just a parentheses but also a\r\n" );
document.write( "plus sign + and a parentheses before the negative term.\r\n" );
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document.write( "That last pair of factors has common monomial factor . If\r\n" );
document.write( "the first term is negative we always take out a negative.\r\n" );
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document.write( "----------------------------\r\n" );
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\n" ); document.write( "Determine the common monomial factor?
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document.write( "We determined them above when we did the grouping. Now we'll factor them \r\n" );
document.write( "all out, so we have:\r\n" );
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document.write( "Notice that when you factor out a negative as in the last\r\n" );
document.write( "parentheses, you change both sign inside the parentheses.\r\n" );
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document.write( "Edwin

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