#### Solitary(OP)

##### Do You Know The Answer?
« on: August 28, 2014, 12:03:46 AM »
"My grandson is about as many days as my son is 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?

"This problem is conveniently solved by writing down the necessary equations. Note that there are 12 months in a year, 52 weeks in a year, and 365 days in a year.

Let m be my age in years. If s is my son's age in years, then my son is 52s weeks old. If g is my grandson's age in years, then my grandson is 365g days old. Thus,

365g = 52s.

Since my grandson is 12g months old,

12g = m.

Since my grandson, my son and I together are 120 years,

g + s + m = 120.

The above system of 3 equations in 3 unknowns (g, s and m) can be solved as follows.

m / 12 + 365 m / (52 × 12) + m = 120 or

52 m + 365 m + 624 m = 624 × 120 or

m = 624 × 120 / 1041 = 72.

So, I am 72 years old."

Food for thought:

Why is the word "about" used in the Problem Statement in the sentence "My grandson is about as many days as my son is weeks"? Calculate the son's age and the grandson's age. Then, verify whether the first equation (i.e., 365g = 52s) is exactly satisfied.

An elegant solution is possible on realizing the significance of the word "about" in the Problem Statement.

Elegant Solution:

The first equation (365g = 52s) can be approximated by

7g = s.

As before, the other two equations are

12g = m

g + s + m = 120.

The above system of 3 equations in 3 unknowns (g, s and m) can be simply solved as follows.

g + 7g + 12g = 120 or 20g = 120.

m = 12g = 12 × 120 / 20 = 72.

So, Grandpa is 72 years old.
« Last Edit: August 28, 2014, 12:05:52 AM by Solitary »
There is nothing more frightful than ignorance in action.

#### GrinningYMIR

##### Re: Do You Know The Answer?
« Reply #1 on: August 28, 2014, 11:44:45 AM »

Interesting problem, but my brain hurts now

*fetal position*
"Human history is a litany of blood shed over differing ideals of rulership and afterlife"

Governor of the 32nd Province of the New Lunar Republic. Luna Nobis Custodit

#### Solitary(OP)

##### Re: Do You Know The Answer?
« Reply #2 on: August 28, 2014, 12:05:49 PM »
I just hated these types of story problems in school because they really do make your brain hurt. Mind is kind of numb now from all my prescription drugs---honestly!  Solitary
There is nothing more frightful than ignorance in action.

#### Green Bottle

##### Re: Do You Know The Answer?
« Reply #3 on: August 28, 2014, 12:16:27 PM »

(Image removed from quote.)

Interesting problem, but my brain hurts now

*fetal position*

I just hated these types of story problems in school because they really do make your brain hurt. Mind is kind of numb now from all my prescription drugs---honestly!  Solitary

I read it again and then i thought , fkit, scroll down an lets see the answer an as i started to read it i thought, mmmmmmm, have i got painkillers...
God doesnt exist, but if he did id tell him to ''Fuck Off''

#### SGOS

##### Re: Do You Know The Answer?
« Reply #4 on: August 28, 2014, 01:09:03 PM »
Yeah, I just said, "Piss on it," and scrolled down to the bottom.

#### PickelledEggs

##### Re: Do You Know The Answer?
« Reply #5 on: August 28, 2014, 01:28:52 PM »
I wasn't able to get that because I'm not a mathmagician
"Tell Pilate to release the files!!!" - Bill Hicks
"I have an open mind, but not so open that my brains will fall out" -James Randi
"One who truly hates himself cannot love, he cannot place his trust in another." - NGE