sum of grandson ,father and grandfather is 110.

Question

the age of grandfather in years is equal to the grandson in months .

the age of father in weeks is equal to the grandson in days

 

Answer 1

Let's first define some variables

S = grandson

F = father

G = grandfather

 

We know from the first sentence that

S + F + G = 110

 

From the 2nd sentence

G = 12S

 

Finally from the 3rd sentence

52F = 365S

 

Since the only variable to appear in all 3 equations is S, lets isolate the variable F in the 3rd equation.  Notice that the variable G is already isolated in equation 2.

52F = 365S

Dividing both sides by 52

F = 7.019S

 

Now let's use the equations for F and G and substitute them into the first equation.  This way the only variable in the 1st equation will be S

S + 7.019S + 12S = 110

 

Combining terms

20.019S = 110

 

Divide both sides by 20.019

5.5 

 

So the grandson is 5.5 years old, which is 66 months

 

Using equation 2,

G = 12S 

G = 12 (5.5) = 66

So the grandfather is 66 years old

 

Finally how old is the father?

Using the first equation again

S + F + G = 110

5.5 + F + 66 = 110

F = 110 - 66 - 5.5 = 38.5

The father is 38.5 years old.