Math Quiz The words are engraved on someone's gravestone. "God gave him his boyhood one-sixth of his life, one-twelfth(1/12) more as a youth while whiskers grew rife; And then yet one-seventh after the marriage has begun; In five years there came a bouncing new son. Alas, the dear child of master and sage After attaining half the measure of his father's life chill fate took him. After consoling his fate by the science of numbers for four years, he ended his life." How many years did he and his son live? And who is 'someone?'. Created by TakenName. Math

12) more as a youth while whiskers grew rife; And then yet one-seventh after the...

Verified answer

★ Concept :-

Here the concept of Algebraic Equation has been used. We see that we are given a word problem to solve and find age of father and son. We can also see that in the qúestion, mostly the relationship of age of father has been described. So we will take age of father as main value and then make the age of son dependent on the age of father. Firstly we shall divide the age of father according to relationship and then add all of them to find the real age of father.

Let's do it

______________________________________

★ Formula Used :-

$\;\boxed{\sf{\pink{Sum\;of\;different\;stages\;of\;age\;=\;\bf{Total\;Age}}}}$

______________________________________

★ Solution :-

Given,

Different stages of age of that person :-

» Time period of life of that person in boyhood = (⅙ × Total Age ) years

» Time period of life of that person as a youth = (1/12 × Total Age) years

» Time period of life of that person after youth and before marriage = (⅐ × Total Age) years

» Time period of life of that person after marriage and before having first child = 5 years

» Time period of life of that person after his child was born and till his child's deáth = (½ × Total age) years

» Time period of life of that person after his child's death and till his death = 4 years

Let the total age of father (that person) be 'p' years (p represent the age of that person) .

Time period of life during boyhood of that person = ⅙ × p

Time period of life during youth of that person 1/12 × p

Time period of life of that person after youth and before marriage = ⅐ × p

Time period of life of that person after marriage and having first child = 5 years

Time period of life of that person after child's birth and till death = ½ × p

Time period of life of that person after his child's death till his death = 4 years

We know that,

$\;\bf{\rightarrow\;\;Sum\;of\;different\;stages\;of\;age\;=\;\bf{Total\;Age}}$

By applying values here, we get

$\;\bf{\rightarrow\;\;\dfrac{1}{6}p\;+\;\dfrac{1}{12}p\;+\;\dfrac{1}{7}p\;+\;5\;+\;\dfrac{1}{2}p\;+\;4\;=\;\bf{p}}$

On rearranging we get,

$\;\bf{\rightarrow\;\;\dfrac{1}{6}p\;+\;\dfrac{1}{12}p\;+\;\dfrac{1}{7}p\;+\;\dfrac{1}{2}p\;+\;5\;+\;4\;=\;\bf{p}}$

$\;\bf{\rightarrow\;\;\dfrac{p}{6}\;+\;\dfrac{p}{12}\;+\;\dfrac{p}{7}\;+\;\dfrac{p}{2}\;+\;5\;+\;4\;=\;\bf{p}}$

LHS of denominators is 84. So,

$\;\bf{\rightarrow\;\;\dfrac{14p}{84}\;+\;\dfrac{7p}{84}p\;+\;\dfrac{12p}{84}\;+\;\dfrac{42p}{84}\;+\;9\;=\;\bf{p}}$

$\;\bf{\rightarrow\;\;\dfrac{14p\;+\;7p\;+\;12p\;+\;42p}{84}\;=\;\bf{p\;-\;9}}$

$\;\bf{\rightarrow\;\;\dfrac{75p}{84}\;=\;\bf{p\;-\;9}}$

Cancelling numerator and denominator of LHS by 3, we get

$\;\bf{\Longrightarrow\;\;\dfrac{25p}{28}\;=\;\bf{p\;-\;9}}$

$\;\bf{\Longrightarrow\;\;25p\;=\;\bf{28(p\;-\;9)}}$

$\;\bf{\Longrightarrow\;\;25p\;=\;\bf{28p\;-\;252}}$

$\;\bf{\Longrightarrow\;\;25p\;-\;28p\;=\;\bf{\;-\;252}}$

$\;\bf{\Longrightarrow\;\;-3p\;=\;\bf{\;-\;252}}$

Cancelling -ve sign from both LHS and RHS, we get

$\;\bf{\Longrightarrow\;\;3p\;=\;\bf{252}}$

$\;\bf{\Longrightarrow\;\;p\;=\;\bf{\dfrac{252}{3}}}$

$\;\bf{\Longrightarrow\;\;p\;=\;\bf{84\;\;years}}$

We know that p is the age of father. So we got the age of father. This means that person lived for 84 years.

$\;\underline{\boxed{\tt{Age\;\:of\;\:Father\;(that\;\:person)\;\:which\;\:he\;\:lived\;=\;\bf{\purple{84\;\;years}}}}}$

We see that in qúestion it is given that child lived half age as his father. So, age of child will be given as ,

→ Age of child = p/2 = 84/2 = 42 years

$\;\underline{\boxed{\tt{Age\;\:of\;\:child\:(son)\;\:of\;that\;\:person\;\:which\;\:he\;\:lived\;=\;\bf{\purple{42\;\;years}}}}}$

These words were written on the gravestone of a famous mathematician Diophantus.

• So here the word someone is used to refer Diophantus.

_______________________________

★ More to know :-

• Algebraic Expression : It is a mathematical equation which is a combination of constant and variable terms of any degree and any number of variables .

• Linear Equations : These are the equations which have constant and variable terms mostly three variables at maximum and the degree of variables is 1.

Linear Equation in One Variable

Linear Equation in Two Variable

Linear Equation in Three Variables

• About Diophantus : He was famous greek mathemetician known for his mental and Algebra solving abilities.

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Step-by-step explanation:

★ Concept :-

Here the concept of Algebraic Equation has been used. We see that we are given a word problem to solve and find age of father and son. We can also see that in the qúestion, mostly the relationship of age of father has been described. So we will take age of father as main value and then make the age of son dependent on the age of father. Firstly we shall divide the age of father according to relationship and then add all of them to find the real age of father.

Let's do it

______________________________________

★ Formula Used :-

$\;\boxed{\sf{\pink{Sum\;of\;different\;stages\;of\;age\;=\;\bf{Total\;Age}}}}$

______________________________________

★ Solution :-

Given,

Different stages of age of that person :-

» Time period of life of that person in boyhood = (⅙ × Total Age ) years

» Time period of life of that person as a youth = (1/12 × Total Age) years

» Time period of life of that person after youth and before marriage = (⅐ × Total Age) years

» Time period of life of that person after marriage and before having first child = 5 years

» Time period of life of that person after his child was born and till his child's deáth = (½ × Total age) years

» Time period of life of that person after his child's death and till his death = 4 years

Let the total age of father (that person) be 'p' years (p represent the age of that person) .

Time period of life during boyhood of that person = ⅙ × p

Time period of life during youth of that person 1/12 × p

Time period of life of that person after youth and before marriage = ⅐ × p

Time period of life of that person after marriage and having first child = 5 years

Time period of life of that person after child's birth and till death = ½ × p

Time period of life of that person after his child's death till his death = 4 years

We know that,

$\;\bf{\rightarrow\;\;Sum\;of\;different\;stages\;of\;age\;=\;\bf{Total\;Age}}$

By applying values here, we get

$\;\bf{\rightarrow\;\;\dfrac{1}{6}p\;+\;\dfrac{1}{12}p\;+\;\dfrac{1}{7}p\;+\;5\;+\;\dfrac{1}{2}p\;+\;4\;=\;\bf{p}}$

On rearranging we get,

$\;\bf{\rightarrow\;\;\dfrac{1}{6}p\;+\;\dfrac{1}{12}p\;+\;\dfrac{1}{7}p\;+\;\dfrac{1}{2}p\;+\;5\;+\;4\;=\;\bf{p}}$

$\;\bf{\rightarrow\;\;\dfrac{p}{6}\;+\;\dfrac{p}{12}\;+\;\dfrac{p}{7}\;+\;\dfrac{p}{2}\;+\;5\;+\;4\;=\;\bf{p}}$

LHS of denominators is 84. So,

$\;\bf{\rightarrow\;\;\dfrac{14p}{84}\;+\;\dfrac{7p}{84}p\;+\;\dfrac{12p}{84}\;+\;\dfrac{42p}{84}\;+\;9\;=\;\bf{p}}$

$\;\bf{\rightarrow\;\;\dfrac{14p\;+\;7p\;+\;12p\;+\;42p}{84}\;=\;\bf{p\;-\;9}}$

$\;\bf{\rightarrow\;\;\dfrac{75p}{84}\;=\;\bf{p\;-\;9}}$

Cancelling numerator and denominator of LHS by 3, we get

$\;\bf{\Longrightarrow\;\;\dfrac{25p}{28}\;=\;\bf{p\;-\;9}}$

$\;\bf{\Longrightarrow\;\;25p\;=\;\bf{28(p\;-\;9)}}$

$\;\bf{\Longrightarrow\;\;25p\;=\;\bf{28p\;-\;252}}$

$\;\bf{\Longrightarrow\;\;25p\;-\;28p\;=\;\bf{\;-\;252}}$

$\;\bf{\Longrightarrow\;\;-3p\;=\;\bf{\;-\;252}}$

Cancelling -ve sign from both LHS and RHS, we get

$\;\bf{\Longrightarrow\;\;3p\;=\;\bf{252}}$

$\;\bf{\Longrightarrow\;\;p\;=\;\bf{\dfrac{252}{3}}}$

$\;\bf{\Longrightarrow\;\;p\;=\;\bf{84\;\;years}}$

We know that p is the age of father. So we got the age of father. This means that person lived for 84 years.

$\;\underline{\boxed{\tt{Age\;\:of\;\:Father\;(that\;\:person)\;\:which\;\:he\;\:lived\;=\;\bf{\purple{84\;\;years}}}}}$

We see that in qúestion it is given that child lived half age as his father. So, age of child will be given as ,

→ Age of child = p/2 = 84/2 = 42 years

$\;\underline{\boxed{\tt{Age\;\:of\;\:child\:(son)\;\:of\;that\;\:person\;\:which\;\:he\;\:lived\;=\;\bf{\purple{42\;\;years}}}}}$

These words were written on the gravestone of a famous mathematician Diophantus.

• So here the word someone is used to refer Diophantus.

_______________________________

★ More to know :-

• Algebraic Expression : It is a mathematical equation which is a combination of constant and variable terms of any degree and any number of variables .

• Linear Equations : These are the equations which have constant and variable terms mostly three variables at maximum and the degree of variables is 1.

Linear Equation in One Variable

Linear Equation in Two Variable

Linear Equation in Three Variables

• About Diophantus : He was famous greek mathemetician known for his mental and Algebra solving abilities.

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