document.write( "Question 1203379: Hi
\n" ); document.write( "Leo and issac had 95 balls together. Leo gave away 3 more than issac. Issac was left with 5 fewer than the balls he gave away. Leo had 2 more balls left than issac. How many did Leo give away.
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Algebra.Com's Answer #838889 by ikleyn(52866) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "(a) Leo and issac had 95 balls together.
\n" ); document.write( "(b) Leo gave away 3 more than issac.
\n" ); document.write( "(c) Issac was left with 5 fewer than the balls he gave away.
\n" ); document.write( "(d) Leo had 2 more balls left than issac.
\n" ); document.write( "How many did Leo give away.
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document.write( "x = Leo had initially\r\n" );
document.write( "y = Issac had initially\r\n" );
document.write( "z = Leo gave away\r\n" );
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document.write( "From (a), we have this equation   x + y = 95.             (1)\r\n" );
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document.write( "From (b), Issac gave away (z-3).\r\n" );
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document.write( "From (c), we have this equation   y - (z-3) = ((z-3)-5),  or   y - 2z = -11   (2)\r\n" );
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document.write( "From (d), we have this equation   x - z = y - (z-3) + 2,  or   x -  y =   5   (3)\r\n" );
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document.write( "Thus, we have this system of equations\r\n" );
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document.write( "    x +  y      =  95    (1)\r\n" );
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document.write( "         y - 2z = -11    (2)\r\n" );
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document.write( "    x -  y      =   5    (3)\r\n" );
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document.write( "Add equations (1) and (3).  Get  2x = 100,  x = 100/2 = 50.    (Leo had initially)\r\n" );
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document.write( "Then from (1),  y = 95 - x = 95 - 50 = 45.                     (Issac had initially)\r\n" );
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document.write( "Then from (2),  2z = y + 11 = 45 + 11 = 56,  z = 56/2 = 28.    (Leo gave away)\r\n" );
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document.write( "ANSWER.  Leo gave away 28 balls.\r\n" );
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document.write( "CHECK.  Issac gave away 28-3 = 25.\r\n" );
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document.write( "        Issac was left with 45 - 25 = 20.\r\n" );
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document.write( "        Leo was left with 50 - 28 = 22.\r\n" );
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document.write( "        Leo left - Issac left = 22 - 20 = 2   (correct).\r\n" );
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