Busy Life Of Santa Claus!

Algebra Level 1

Here is a difficult word problem I am struggling with:
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?

Image credit: Wikipedia


The answer is 75.

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37 solutions

Amulya Pokala
Mar 8, 2014

let the working life of santa be 'x' years...x=(x/3+x/4+x/5)+13. from this equation, we get x=60. as santa started working at 15, his age will be 15+60=75.

let the age of santa=x; then his working age=(x-15); so, (x-15)=((x-15)/3+ (x-15)/4+(x-15)/5)+13; from this we get x=75; therefore age of the santa is75

Akash Saurabh - 7 years, 2 months ago

actually i just add up the fractions and it's 47/60. since his last working years were 13 , the denominator for 47 is 60 and 60-47 is 13. 47 years were the part of his life he worked other jobs. 47 is a fraction of 60 which is a whole. And that would mean that that whole is 60. 47 years plus 13 years we got 60 years. 60 years plus 15 years equals to 75 years

Wing-wing Arcenal - 7 years, 2 months ago

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i used the same solution as well.

Ratan Paul - 7 years, 2 months ago

I used the same solution too. Yeay! :D

Angelia Yulita - 7 years, 2 months ago

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

Huna Luna - 7 years, 2 months ago

i used the same method :D

Tetris Battle Sender - 7 years, 2 months ago

i thnk the same :D

Fatima Zaheer - 7 years, 2 months ago

nice and neat solution :)

Erica Paham - 7 years, 2 months ago

What is the biggest prime number ?

Mahesh Krishna Bheemanapalli - 7 years, 2 months ago

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its impossible to find the biggest prime no....i think

Binay Kumar - 7 years, 2 months ago

Since there is an infinite number of numbers, then there is an infinite number of prime numbers an no biggest one.

Alexandra Polyakova - 7 years, 2 months ago

ok

Khadim Hussain - 7 years, 2 months ago

well solved

zalmey khan - 7 years, 2 months ago

same solution age = 75 :)

usaman azeem - 7 years, 2 months ago

i got the logic but made a silly mistake... Good question...

Krishna Mohan - 7 years, 2 months ago

i solve in little different way like,(x/3+x/4+x/5)=x-13

Khushyal Singh - 7 years, 2 months ago

it is same

Khushyal Singh - 7 years, 2 months ago

after finding 'x' +15

Khushyal Singh - 7 years, 2 months ago

i got thhe logi but made a minure mistake

aditya ms - 7 years, 2 months ago

well, he is old enough to tell 8-years old girl this riddle :P

Ahmad Magdy - 6 years, 9 months ago

i don't understand this type of questions

Muhammad Mubashar Nazeer - 7 years, 2 months ago

that's not coming exact 60, x=x/3+x/4+x/5+13=> x=0.78x+13=> x=13/0.22=59.09 check it please

anju saxena - 7 years, 2 months ago

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1/3 + 1/4 + 1/5 = 47/60...not .78 This is a small difference, but it is the source of your error.

Jeff Downin - 7 years, 2 months ago

keep it in fraction..

Angshuman Banik - 7 years, 2 months ago

y?

Abhijith Radhakrishnan - 7 years, 2 months ago

no error...

shivendra shukla - 7 years, 2 months ago

Hm? So did you do this? 5•4=20, 20•3=60, 60+15?

Niya Monae - 7 years, 2 months ago

nice question

J Fan - 7 years, 2 months ago

nice amulya

Barjees Babar - 7 years, 3 months ago
Chết Chắc
Mar 20, 2014

Call x = Santa's working years, we have:

1 4 x + 1 5 x + 1 3 x + 13 = x \frac{1}{4}x + \frac{1}{5}x + \frac{1}{3}x + 13 = x 47 60 x + 13 = x \frac{47}{60}x + 13 = x 13 = 13 60 x 13 = \frac{13}{60}x x = 60 x = 60

so, Santa's age equal to: 15 + x <=> 15 + 60 = 75

can you clear the step of 47 how you got it ? can you explain more in detail ?

Syed Noman Ahmed - 7 years, 2 months ago

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If you add 1/3, 1/4 and 1/5 together you get 47/60

Connor Quinn - 7 years ago

can u explain how 47 becomes 13.

Muthu Karthick - 7 years, 2 months ago

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Take the x terms together, then it would be (60-47)/60

Collin Fernandes - 7 years ago
Syed Imad Azeem
Mar 11, 2014

let the age of santa = y
let the working life of santa = x
So
y=x+15 .............(1)
x=(x/3)+(x/4)+(x/5)+13.................(2)



solve equation no. 2
x=60
subsitute this value of x in equation no.1
y=(60)+15
y=75
therefor age of santa = 75

yup.. of course...

Ersa Desmelinda - 7 years, 2 months ago

yaa....

Kasfia Chowdhury - 7 years, 2 months ago
Majharul Haque
Mar 20, 2014

1/4+1/5+1/3=47/60 remaining = 13/60, so working life = 60, so total age=60+15=75

Natsu Jett
Jun 3, 2014

4times5times3=60 60+15=75

Swarali Patil
May 3, 2014

The total time spent by Santa in working = x.
Therefore, x = x/3 + x/4 + x/5 + 13.
Therefore, x=60.
Thus, Santa's total age = 60+15 =75.
Ans: 75 years.


Bidyut Das
Apr 8, 2014

(1/4 + 1/5 +1/3)*60 + 15+28=75

Christian Uy
Apr 7, 2014

75 years old

Ameya Salankar
Apr 5, 2014

Let x x be the working life of Santa in years. Then he spent,

x 4 \frac{x}{4} of his working life in the factory, x 5 \frac{x}{5} of his working life in the office & x 3 \frac{x}{3} of his working life as a caretaker. And for the last 13 13 years of his working life, he had been Santa. So we get the following equation :

x 4 + x 5 + x 3 = x 13 \frac{x}{4} + \frac{x}{5} + \frac{x}{3} = x - 13

Solving this, we get x = 60 x = 60 .

But he started working at the age of 15 15 years.

\Rightarrow His age is 15 + 15 + his working life.

\Rightarrow 15 + 60 = 75 15 + 60 = \boxed{75} .

Add up the fractional work experience and subtract from one to determine the fractional work experience as a Santa

i.e. 13 1 1 4 + 1 5 + 1 5 \frac{13}{ 1 - \frac{1}{4} + \frac{1}{5} + \frac{1}{5} }

13 13 60 = 60 \Rightarrow \frac{13}{\frac{13}{60}} = 60

So his age is 60 + 15 = 75

Amogh Jain
Mar 30, 2014

x=(x/3+x/4+x/5), we get x is 60 and 60+15=75

Raja Birbol
Mar 29, 2014

say,his total working life is x years.so (x\4)+(x\5)+(x\3)+13=X.then X=60.so he is 60+15=75 years old.

say,his total working life is x years.so (x\4)+(x\5)+(x\3)+13=X.then X=60.so he is 60+15=75 years old.

Louella Mamuyac
Mar 29, 2014

x = x/4 + x/5 + x/3 + 13, so x = 60.. then 60 + 15 = 75!!!

Narendra Kumar
Mar 27, 2014

take the L.C.M of 4,5,3 and add 15 to it answer will be 60+15=75

Paritosh Malhotra
Mar 27, 2014

Let x be the total working age. Then: 1/5x + 1/4x + 1/3x + 13 = x => x =60 He worked since he was 15 So total age =(60+15) = 75 years.

Miciah Amberong
Mar 27, 2014

Age = 15 + (x/4 + x/5 + x/3 + 13)

or

Age = 15 + x

where x = Working Life

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

x = 9x/20 + x/3 +13

x = 47x/60 + 13

x - 47x/60 = (47x/60 - 47x/60) + 13

13x/60 = 0 + 13

13x/60 = 13

(13x/60) * 60 = 13 * 60

13x = 13 * 60

13x/13 = (13 * 60)/13

x = 1 * 60

x = 60

Age = 15 + 60

Age = 75

Afzal Sajid
Mar 26, 2014

in the question the santa's age is show as 1.So we get the 1 as santa age. his work started age 15. the age from he did't work 13. 1=(1÷3,1÷4,1÷5)+13 from this we get 1=60 we get all ages except 15 so we add the work start age 60+15=75 So 1=75.So santa's age is 75 :)

Vikas Kumar
Mar 24, 2014

let the working age of santa be X. Then his present age would be X+15. So, let's calculate his working age, i.e, X/4 + X/5 + X/3 + 13 = X => X=60. So, his present age = X+15=60+15=75.

Binay Kumar
Mar 24, 2014

let the age of the santa clause be x now, (x-15)=(x-15)/4+(x-15)/5+(x-15)/3 +13 implies that,x=75 years

Asad Abbas
Mar 24, 2014

let age of santa is=x,then x=x/4+x/5+x/3,we get x=60.hence his age will be=working age+15,which is =75.

Himanshu Ranjan
Mar 24, 2014

here , let x/4 life in factory , x/5 in other and x/3 in any other so adding this we get 47x/60 so 47 years in all these works and 13 years as santa and 15 years as child so 15+13+47=75 years..that's it

Shiva Shankar
Mar 22, 2014

Let x be the working life so (1/4)x + (1/5)x + (1/3)x + 13 = x. Solve and eventually you will get 13x = 780. Solving this you will get x = 60. Then add 15 and you will get age as 75.

Shuja Amjad
Mar 22, 2014

get the L.C.M of the 3 values 4,5,3 which are the denominators of the fractions the answer will be 60 hence we get the fractions 15/60, 20/60 , 12/60 add these fractions : 47 / 60 subtract from 1 the above fraction now we form an algebric equation: 13/ 60 * (X-15) = 13

Nour El Shaarawy
Mar 21, 2014

1/4 + 1/5 + 1/5 = 47/60 , Since the last 13 years of his life represent 13/60, Therefore, his working life= 47 + 13= 60. Therefore, his age= 15 + 60=75 years #

Archi Jaiswal
Mar 21, 2014

consider total working life as x..........find solution and add 15 to know his age

Mahendar Singh
Mar 21, 2014

(1-(1/4+1/5+1/3))*X = 13

X=13/(1-(47/60))

X= 13/(13/60)

X=60

work life = 60

Age = work life + age during start of work Age= 60+15 Age =75

Adwait Rane
Mar 21, 2014

Let Santa's work Life be x. Then x=(1/3+1/4+1/5). The answer in decimal form is 0.78. so he spent 78% of his life as working in Factory,Office and as School caretaker. Now the remaining working life is 22%. We know that he spent 13 years of his remaining working life as SANTA. so 22% of x is equal to 13. Thus we get x=60. Now since he started working at 15. His age would be x+15 that is 60+15= 75. This is how i got to the answer.(There is a small error in the question that x =59.09. If we round off it it becomes 59. thus 59+15=74. So the correct answer should have been 74)

Sunil Pradhan
Mar 20, 2014

1/4 + 1/5 + 1/3 = 13/60 remaining years = 1/1 – 13/60 = 13/60 so 13/60 part = 13 years then 1 part = 60/13 × 13 = 60

age = 15 + 60 = 75 years

Geet Singh
Mar 19, 2014

Let total age of Santa be x, 15 years no work. So Working Life = x-15.

Equation is - 15 + 13 + (x-15)/4 + (x-15)/5 + (x-15)/3 = x

Akash Saurabh
Mar 19, 2014

let the age of santa=x; then his working age=(x-15); so, (x-15)=((x-15)/3+ (x-15)/4+(x-15)/5)+13; from this we get x=75; therefore age of the santa is75

Khandakar Rahman
Mar 19, 2014

Let the total working life is 'x' As per x-(x/3+x/4+x/5)=13 we can find x=60 Total life will be, 15+60 = 75

Jia Quan Ng
Mar 19, 2014

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

So, he has spent 13 years of his working life to be Santa Claus

60/60 - 47/60 = 13/60

1 year=1/60

60years=60/60 60years+15years=75 years

Are you assuming that he must have working for 60 years?

Calvin Lin Staff - 7 years, 2 months ago

where did you get 47?

Kirk Hammet - 7 years, 2 months ago
Jaypee Reynoso
Mar 18, 2014

Let X be his working life...

First, you have to find the value of X and it will be possible if you deduct the WHOLE WORKING life with the given Fraction giving a remaining working life which is 13

Illustration:

X - (47/60)(X) = 13 (13/60)(X) = 13 X = 60

Then, to get his present age, add his working life with his age when he started working

15 + 60 = 75 ;)

Krishna Garg
Mar 18, 2014

Started working at 15 yrs of age, suppose age is X yrs add X-15/4 + x-15/5 + X-15/3 + 15 +13 will be equal to X simplifying above we get 75 yrs Ans

K.K.GARG,India

Assume that his working life is x x years.

Now from the question we can derive the equation that,

x 1 4 + x 1 5 + x 1 3 + 13 = x x\frac{1}{4}+x\frac{1}{5}+x\frac{1}{3}+13=x

from this equation we find the value of x x is 60 60

He started the job at the age of 15 15 , so he is 75 75 .

Yaseen Khan
Mar 18, 2014

let the working life of Santa is x. so the equations becomes x= x/3+x/4+x/5 comes out to be 60. than simply add 15 to it.

Why didn't we add 15 rhough..?

Jassehaj Singh - 7 years ago

i agree

Wezley Skelton - 7 years, 2 months ago

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