Even Santa is clever!!!

Algebra Level 2

8-year-old Samantha visited Santa at a local department store. He gave her this riddle: " I started working at 15. I spent 1/4 of my working life in a factory. I spent 1/5 of my working life in an office, and I spent 1/3 of my working life as a school caretaker. For the last 13 years of my working life I've been Santa Claus. How old am I?" Help Samantha find his age.


The answer is 75.

Tanveen Dhingra by tanveen dhingra , 19, India

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2 solutions

Tanveen Dhingra
Oct 20, 2014

Let "x" be the number of working-life years. factory time: (1/4)x

office time : (1/5)x

school time : (1/3)x

Santa time : 13 years

Working-life equation: (1/4)x + (1/5)x + (1/3)x + 13 = x

15x + 12x + 20x + 60*13 = 60x

47x + 60*13 = 60x

13x = 60*13

x = 60 (years he worked)

Age = 15 + 60 = 75 yrs. old

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Mehul Arora
Oct 24, 2014

Let x be the total number of years he has worked

Hence, No. of years he worked in a factory=(1/4x)

No. of years he worked in the office=(1/5x)

No. of years he worked a school caretaker=(1/3x)

Adding the number of years x-(47/60x)= 13years

Which implies that x=60 years

Hence, Santa has been working for 60 years

And since it is given that he started working a the age of 15, His age =60+15 years=75 Years

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