document.write( "Question 1023844: 4 years ago, the age difference of a father and son is 7 times. 16 years hence, it would be 2 times . Find their current ages. Please help \n" ); document.write( "

Algebra.Com's Answer #639332 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "4 years ago, the age $\"highlight%28cross%28difference%29%29\"$ ratio of a father and son was 7 times. 16 years hence, it would be 2 times. Find their current ages. Please help
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document.write( "1.  Notice I changed your incorrect formulation.\r\n" );
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document.write( "2.  Let f = father's present age; s = son's present age.\r\n" );
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document.write( "    Then 4 years ago the father's age was f - 4; the son's age was s - 4, and\r\n" );
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document.write( "     = 7.    (1)\r\n" );
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document.write( "    In 16 years the father's age will be f + 16; the sons age will be s + 16, and\r\n" );
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document.write( "     = 2.   (2)\r\n" );
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document.write( "    You need to solve this system of two equations in two unknowns (1) and (2).\r\n" );
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document.write( "3.  Let us simplify it. Multiply (1) by (s-2) (both sides). Multiply (2) by (s+16) (both sides). You will get\r\n" );
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document.write( "    f -  4 = 7*(s-4),     (3)\r\n" );
document.write( "    f + 16 = 2*(s+16).    (4)\r\n" );
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document.write( "    Next express f = 7*(s-4) + 4 from (3) and substitute it into (4). You will get\r\n" );
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document.write( "    7*(s-4) + 4 + 16 = 2*(s+16).\r\n" );
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document.write( "    Simplify it step by step:\r\n" );
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document.write( "    7s - 28 + 4 + 16 = 2s + 32,\r\n" );
document.write( "    7s - 2s = 32 + 28 - 4 - 16,\r\n" );
document.write( "    5s = 40,\r\n" );
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document.write( "    s =  = 8.\r\n" );
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document.write( "    Hence, son is 8 years now.\r\n" );
document.write( "    Then father's age is f = 7*(s-4)+4 = 7*4+4 = 32.\r\n" );
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document.write( "Answer. Father's present age is 32 years. Son's present age is 8 years.\r\n" );
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