My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 120 years. Can you tell me my age in years ?

MathsGod1
Mar 23, 2015

#5**+15 **

My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 120 years. Can you tell me my age in years ?

I'm assuming a 30 day month and a 360 day year in this problem...other assumptions may produce "round numbers" at the end..(I don't know, and don't really care)..but...we'll get close enough...besides...it's the idea of the thing that counts......

Let the son's age in years be x

Then, the son's age in weeks= 52 weeks per year times the number of years he has lived = 52x = the grandson's age in days

The grandson's age in months is (assuming a 30 day month) = the number of days he has lived/30 days in a month = (52x)/30. So the grandson's age in years = (52x)/(12months*30 days in a month) = (52x)/360

Let the grandfather's age in years = y And this = the grandson's age in months

So y = (52x)/30 ....and we have

The son's age in years + the grandson's age in years + the grandfather's age in years = 120 ...or....

x + (52x)360 + (52x)/30 = 120

[360x + 52x + 624x] = 43200

[1036]x = 43200

x = 41.7 years = and this is the son's age...we'll call it 42

And the grandson's age iin years = (52*41.7)/ 360 = about 6 years old

And the grandfather's age is (52*41.7)/ 30 = about 72.28 years....and we'll call this 72

So

42 + 6 + 72 =

48 + 72 =

120

Close enough!!!

CPhill
Mar 25, 2015

#2**0 **

Lol.

Same with me, questions worded like this make my brain explode!

Too much to take in!!!

MathsGod1
Mar 24, 2015

#5**+15 **

Best Answer

My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 120 years. Can you tell me my age in years ?

I'm assuming a 30 day month and a 360 day year in this problem...other assumptions may produce "round numbers" at the end..(I don't know, and don't really care)..but...we'll get close enough...besides...it's the idea of the thing that counts......

Let the son's age in years be x

Then, the son's age in weeks= 52 weeks per year times the number of years he has lived = 52x = the grandson's age in days

The grandson's age in months is (assuming a 30 day month) = the number of days he has lived/30 days in a month = (52x)/30. So the grandson's age in years = (52x)/(12months*30 days in a month) = (52x)/360

Let the grandfather's age in years = y And this = the grandson's age in months

So y = (52x)/30 ....and we have

The son's age in years + the grandson's age in years + the grandfather's age in years = 120 ...or....

x + (52x)360 + (52x)/30 = 120

[360x + 52x + 624x] = 43200

[1036]x = 43200

x = 41.7 years = and this is the son's age...we'll call it 42

And the grandson's age iin years = (52*41.7)/ 360 = about 6 years old

And the grandfather's age is (52*41.7)/ 30 = about 72.28 years....and we'll call this 72

So

42 + 6 + 72 =

48 + 72 =

120

Close enough!!!

CPhill
Mar 25, 2015