Please Solve

Question

Demochares has lived one-fourth of his life as a boy, one-fifth as a youth, one-third as a man, and has spent thirteen years in his dotage. How old is the gentleman?

Answer 1

Let Age be the age of the man.  He spent:

one fourth as a boy = (1/4)*Age

one-fifth as a youth = (1/5)*Age

one-third as a man = (1/3)*Age

13 years in his dotage = 13

 

Age = (1/4)*Age + (1/5)*Age + (1/3)*Age + 13 years

 

Let's put the fractions (1/4, 1/5, 1/3) over a common denominator (60) and add them together:

 

Age = (15/60)*Age + (12/60)*Age + (20/60)*Age + 13

 

Age = (47/60)*Age + 13

 

Age - (47/60)*Age = 13         [Subtract (47/60)*Age from both sides]

 

(13/60)*Age = 13

 

Age = 13*(60/13)                  [Multiply both sides by 60/13]

 

Age = 60 years

 

Tell your teacher, BTW, that 60 years old is not "dotage"!   ;-P

Answer 2

1/4 + 1/5 + 1/3 = 47/60

 

That leaves 13/60 of age is 13 years.

 

(13/60)x = 13

 

x = 60

 

He is 60 years old now

Answer 3

karen

 

you posted the same exact question yesterday and 2 tutors provided answers. I gave you the answer 60. Not sure why it was necessary to post the same question again.

Answer 4

Let x = his current age

1/4 x + 1/5 x + 1/3 x + 13 = x

0.25x + 0.2x + 0.33x + 13 = x

0.78x + 13 = x

13 = 0.22x

x = 59.1 years 

 

1/4 as a boy = ~14.8 years as a boy

1/5 as a youth = ~ 11.8 years as a youth

1/3 as a man = ~19.7 years as a man

dotage = 13 years