document.write( "Question 1036524: Hi there,\r
\n" ); document.write( "\n" ); document.write( "I was given the following problem and I just can't figure it out. Could you please let me know how to come up with the answer? Thanks!\r
\n" ); document.write( "\n" ); document.write( "Given these facts: Jack's age plus Marie's age is 27; Jack's age plus Fred's age is 38; Marie's age plus Fred's age is 33. How old is Jack? \n" ); document.write( "

Algebra.Com's Answer #651204 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Hi there,\r
\n" ); document.write( "\n" ); document.write( "I was given the following problem and I just can't figure it out. Could you please let me know how to come up with the answer? Thanks!
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\n" ); document.write( "Given these facts: Jack's age plus Marie's age is 27; Jack's age plus Fred's age is 38; Marie's age plus Fred's age is 33. How old is Jack?
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document.write( "Let j, m, f be their ages.  Then\r\n" );
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document.write( "j + m = 27,    (1)\r\n" );
document.write( "j + f = 38,    (2)\r\n" );
document.write( "m + f = 33.    (3)\r\n" );
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document.write( "The method to solve this system is as follows.\r\n" );
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document.write( "Add equations (1), (2) and (3) (both left sides and right sides). You will get\r\n" );
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document.write( "2*(j + m + f) = 27 + 38 + 33 = 98,   or\r\n" );
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document.write( "j + m + f = 49.    (4)     ( <<<--- 49 =  )\r\n" );
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document.write( "Now, distract equation (1) from (4). You will get\r\n" );
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document.write( "f = 49 - 27 = 22.\r\n" );
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document.write( "Next, distract equation (2) from (4). You will get\r\n" );
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document.write( "m = 49 - 38 = 11.\r\n" );
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document.write( "Finally, distract equation (3) from (4). You will get\r\n" );
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document.write( "j = 49 - 33 = 16.\r\n" );
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document.write( "Answer.  Jack is 16,  Marie is 11,  and  Fred is 22.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The lesson to learn from this solution is this trick for solving this special system of equations.\r
\n" ); document.write( "\n" ); document.write( "Actually, it is the method which works in many other similar cases. See the lessons\r
\n" ); document.write( "\n" ); document.write( " - The tricks to solve some word problems with three and more unknowns using mental math \r
\n" ); document.write( "\n" ); document.write( " - Joint-work problems for 3 participants (Problem 2)\r
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