Question

The present age of a woman is 3 years more than three times the age of her daughter. Three years hence, the womans age will be 10 years, more than twice the age of her daughter. Find their present ages.​

Answer 1

${\Large\mathfrak \orange{Given}}\begin{cases}\sf\gray{The\: present\: age\: of\: a \:woman\: is \:3 \:years\: more\: than \:three \:times \:the \:age \:of \:her\: daughter.} \\ \sf\gray{Three\: years\: hence, \:the \:womans \:age\: will \:be \:10 \:years, \:more \:than\: twice\: the\: age\: of\: her \:daughter.} \end{cases}$

${\Large \mathfrak \green{To\:Find}}\begin{cases}\sf\blue{Present \ ages \ of woman \ \& \ daughter}\end{cases}$

$\huge\bf\red{\underline{\underline{Solution}}}\::$

$\bf \pink{Let}\begin{cases}\sf\underline\gray{Present \ age \ of \ woman \ = \ x } \\ \sf\underline\gray{Present \ age \ of \ daughter \ = \ y }\end{cases}$

$\to\:\:\:\sf\purple {x \:=\:3\:+\:3y}$

$\to\:\:\:\sf\green{x \:-\:3y\:=\:3........(1)}$

$\sf\underline\orange{3\:years\:hence,}$

$\mapsto\:\:\:\sf\purple {x \:+\:3\:=\:10\:+\:2(y\:+\:3)}$

$\mapsto\:\:\:\sf\green {x \:+\:3\:=\:10\:+\:2y\:+\:6}$

$\mapsto\:\:\:\sf\purple {x \:-\:2y\:=\:13........(2)}$

$\sf\underline\orange{Subtracting \::-\:eq(1)\:-\:eq(2)}$

$\hookrightarrow\:\:\:\sf\purple {-y\:=\:-10}$

$\hookrightarrow\:\:\:{\boxed{\sf{\green {y\:=\:10}}}}$

$\sf\underline\orange{Woman's \ age }\::$

$\leadsto\:\:\:\sf\purple {x \:=\:3\:+\:3y}$

$\leadsto\:\:\:\sf\green {x \:=\:3\:+\:3(10)}$

$\leadsto\:\:\:{\boxed{\sf{\purple {x\:=\:33}}}}$

$\bf \blue{Hence}\begin{cases}\star\:\sf\underline\red{Present\:age\:of\: woman\:=\:33\:years}\\\star\:\sf\underline\red{Present\:age\:of\: daughter\:=\:10\:years}\end{cases}$