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Question Number 40299 by mondodotto@gmail.com last updated on 18/Jul/18
the present age of the son is ten years  less than twice that of his father.  if the sum of their age is 80 years.  find the age of the father
$$\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{present}}\:\boldsymbol{\mathrm{age}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{son}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{ten}}\:\boldsymbol{\mathrm{years}} \\ $$$$\boldsymbol{\mathrm{less}}\:\boldsymbol{\mathrm{than}}\:\boldsymbol{\mathrm{twice}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{his}}\:\boldsymbol{\mathrm{father}}. \\ $$$$\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{their}}\:\boldsymbol{\mathrm{age}}\:\boldsymbol{\mathrm{is}}\:\mathrm{80}\:\boldsymbol{\mathrm{years}}. \\ $$$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{age}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{father}} \\ $$
Answered by MJS last updated on 18/Jul/18
father′s age =x  son′s age =2x−10  x+2x−10=80  3x=90  x=30  2x−10=50  so the son is 20 years older than his father.  is this the typical out−of−life−example?  or maybe a case of rebirth?
$$\mathrm{father}'\mathrm{s}\:\mathrm{age}\:={x} \\ $$$$\mathrm{son}'\mathrm{s}\:\mathrm{age}\:=\mathrm{2}{x}−\mathrm{10} \\ $$$${x}+\mathrm{2}{x}−\mathrm{10}=\mathrm{80} \\ $$$$\mathrm{3}{x}=\mathrm{90} \\ $$$${x}=\mathrm{30} \\ $$$$\mathrm{2}{x}−\mathrm{10}=\mathrm{50} \\ $$$$\mathrm{so}\:\mathrm{the}\:\mathrm{son}\:\mathrm{is}\:\mathrm{20}\:\mathrm{years}\:\mathrm{older}\:\mathrm{than}\:\mathrm{his}\:\mathrm{father}. \\ $$$$\mathrm{is}\:\mathrm{this}\:\mathrm{the}\:\mathrm{typical}\:\mathrm{out}−\mathrm{of}−\mathrm{life}−\mathrm{example}? \\ $$$$\mathrm{or}\:\mathrm{maybe}\:\mathrm{a}\:\mathrm{case}\:\mathrm{of}\:\mathrm{rebirth}? \\ $$

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