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Question Number 41086 by byaw last updated on 01/Aug/18
A woman is four times older than   her daughter. Six years ago the  product of their ages is 136.  How old is the woman?
$$\mathrm{A}\:\mathrm{woman}\:\mathrm{is}\:\mathrm{four}\:\mathrm{times}\:\mathrm{older}\:\mathrm{than}\: \\ $$$$\mathrm{her}\:\mathrm{daughter}.\:\mathrm{Six}\:\mathrm{years}\:\mathrm{ago}\:\mathrm{the} \\ $$$$\mathrm{product}\:\mathrm{of}\:\mathrm{their}\:\mathrm{ages}\:\mathrm{is}\:\mathrm{136}. \\ $$$$\mathrm{How}\:\mathrm{old}\:\mathrm{is}\:\mathrm{the}\:\mathrm{woman}? \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 01/Aug/18
woman=4x  daughtet=x  (4x−6)(x−6)=136  4x^2 −24x−6x+36−136=0  4x^2 −30x−100=0  4x^2 −40x+10x−100=0  4x(x−10)+10(x−10)=0  (x−10)(4x+10)=0  x=10 daughter age  woman ave=40
$${woman}=\mathrm{4}{x}\:\:{daughtet}={x} \\ $$$$\left(\mathrm{4}{x}−\mathrm{6}\right)\left({x}−\mathrm{6}\right)=\mathrm{136} \\ $$$$\mathrm{4}{x}^{\mathrm{2}} −\mathrm{24}{x}−\mathrm{6}{x}+\mathrm{36}−\mathrm{136}=\mathrm{0} \\ $$$$\mathrm{4}{x}^{\mathrm{2}} −\mathrm{30}{x}−\mathrm{100}=\mathrm{0} \\ $$$$\mathrm{4}{x}^{\mathrm{2}} −\mathrm{40}{x}+\mathrm{10}{x}−\mathrm{100}=\mathrm{0} \\ $$$$\mathrm{4}{x}\left({x}−\mathrm{10}\right)+\mathrm{10}\left({x}−\mathrm{10}\right)=\mathrm{0} \\ $$$$\left({x}−\mathrm{10}\right)\left(\mathrm{4}{x}+\mathrm{10}\right)=\mathrm{0} \\ $$$${x}=\mathrm{10}\:{daughter}\:{age} \\ $$$${woman}\:{ave}=\mathrm{40} \\ $$
Commented by byaw last updated on 02/Aug/18
thank you very much.
$${thank}\:{you}\:{very}\:{much}. \\ $$

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