document.write( "Question 1208364: Alan the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Monday there were 2 clients who did Plan A and 5 who did Plan B. On Tuesday there were 8 clients who did Plan A and 3 who did Plan B. Alan trained his Monday clients for a total of 8 hours and his Tuesday clients for a total of 15 hours. How long does each of the workout plans last? \n" ); document.write( "

Algebra.Com's Answer #846743 by ikleyn(52872) $\"\"$ $\"About$

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\n" ); document.write( "Alan the trainer has two solo workout plans that he offers his clients: Plan A and Plan B.
\n" ); document.write( "Each client does either one or the other (not both).
\n" ); document.write( "On Monday there were 2 clients who did Plan A and 5 who did Plan B.
\n" ); document.write( "On Tuesday there were 8 clients who did Plan A and 3 who did Plan B.
\n" ); document.write( "Alan trained his Monday clients for a total of 8 hours and his Tuesday clients for a total of 15 hours.
\n" ); document.write( "How long does each of the workout plans last?
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document.write( "Let \"a\" be the hours for plan A;\r\n" );
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document.write( "    \"b\" be the hours for plan B.\r\n" );
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document.write( "As you read the problem, write two equations\r\n" );
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document.write( "    2a + 5b =  8    (1)    (Monday hours)\r\n" );
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document.write( "    8a + 3b = 15    (2)    Tuesday hours)\r\n" );
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document.write( "So, you have this system of two equations in two unknown.\r\n" );
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document.write( "To find \"a\" and \"b\", solve it using the Elimination method.\r\n" );
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document.write( "For it, multiply equation (1) by 4;  kepp equation (2) as is.\r\n" );
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document.write( "New system is\r\n" );
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document.write( "    8a + 20b = 32,    (1')\r\n" );
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document.write( "    8a +  3b = 15.    (2')\r\n" );
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document.write( "From eq.(2') subtract eq.(1').  You will get\r\n" );
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document.write( "          20b - 3b = 32 - 15\r\n" );
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document.write( "              17b  =    17\r\n" );
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document.write( "                b  =    17/17 = 1.\r\n" );
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document.write( "So, plan B is 1 hour.\r\n" );
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document.write( "To find \"a\" substitute b= 1 into equation (1)\r\n" );
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document.write( "    2a + 5*1 = 8\r\n" );
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document.write( "    2a = 8 - 5 = 3\r\n" );
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document.write( "     a =         3/2 = 1.5.\r\n" );
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document.write( "ANSWER.  Plan A is 1.5 hours.  Plan B is 1 hour.\r\n" );
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