document.write( "Question 1178678: Let a, b, and c be integers that satisfy 2a + 3b = 52, 3b + c = 41, and bc = 60. Find a+b+ c. \n" ); document.write( "

Algebra.Com's Answer #808020 by MathLover1(20849) $\"\"$ $\"About$

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\n" ); document.write( " $\"2a+%2B+3b+=+52\"$ ...........eq.1
\n" ); document.write( " $\"3b+%2B+c+=+41\"$ ...........eq.2
\n" ); document.write( " $\"bc+=+60\"$ ...........eq.3
\n" ); document.write( "-----------------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Find $\"a%2Bb%2B+c\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"3b+%2B+c+=+41\"$ ...........eq.2, solve for $\"c\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+c+=+41-3b\"$ ...........eq1)\r
\n" ); document.write( "\n" ); document.write( " $\"bc+=+60\"$ ...........eq.3, solve for $\"c\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"c+=+60%2Fb\"$ ................2)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "from 1) and 2) we have\r
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\n" ); document.write( "\n" ); document.write( " $\"++41-3b=60%2Fb\"$ ........solve for $\"b\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"++41b-3b%5E2=60\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"++0=3b%5E2-41b%2B60\"$ ....factor\r
\n" ); document.write( "\n" ); document.write( " $\"+++%28b+-+12%29+%283b+-+5%29=0\"$ \r
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\n" ); document.write( "\n" ); document.write( "solutions:\r
\n" ); document.write( "\n" ); document.write( " $\"b=12\"$
\n" ); document.write( "or
\n" ); document.write( " $\"b=5%2F3\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "go to\r
\n" ); document.write( "\n" ); document.write( " $\"+c+=+41-3b\"$ ...........eq1), substitute $\"b\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+c+=+41-3%2A12\"$
\n" ); document.write( " $\"+c+=+5\"$ \r
\n" ); document.write( "\n" ); document.write( "or\r
\n" ); document.write( "\n" ); document.write( " $\"+c+=+41-3%2A%285%2F3%29\"$
\n" ); document.write( " $\"+c+=+36\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "so we have two pairs of solutions for $\"b\"$ and $\"c\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"b=12\"$ , $\"+c+=+5\"$
\n" ); document.write( "and
\n" ); document.write( " $\"b=5%2F3\"$ , $\"+c+=+36\"$ \r
\n" ); document.write( "\n" ); document.write( "go to\r
\n" ); document.write( "\n" ); document.write( " $\"2a+%2B+3b+=+52\"$ ...........eq.1, substitute $\"b=12\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2a+%2B+3%2A12+=+52\"$
\n" ); document.write( " $\"2a+%2B+36=+52\"$
\n" ); document.write( " $\"2a+=+52-36\"$
\n" ); document.write( " $\"2a+=+16\"$
\n" ); document.write( " $\"a+=+8\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "one solution is: $\"highlight%28a+=+8%29\"$ , $\"highlight%28b=12%29\"$ , $\"+highlight%28c+=+5%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "then $\"a%2Bb%2B+c=8%2B12%2B5=25\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"2a+%2B+3b+=+52\"$ ...........eq.1, substitute $\"b=5%2F3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2a+%2B+3%2A%285%2F3%29=+52\"$
\n" ); document.write( " $\"2a+%2B+5=+52\"$
\n" ); document.write( " $\"2a+=+52-5\"$
\n" ); document.write( " $\"2a+=+47\"$
\n" ); document.write( " $\"a+=+47%2F2\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "other solution is: $\"highlight%28a+=+47%2F2%29\"$ , $\"highlight%28b=5%2F3%29\"$ , $\"+highlight%28c+=+36%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "then $\"a%2Bb%2B+c=47%2F2%2B5%2F3%2B36=367%2F6=61%261%2F6\"$ \r
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