Question

The age of Jack is thrice the sum of the ages of his two friends, and 5 years hence his age will be twice the sum of their ages. Find the present age of Jack

How do I do this problem
Please Explain

Answer 1

Answer:

The present Age of Jack is 45 years  .

Step-by-step explanation:

Given as :

Let The present age of Jack = x years

Statement I

The age of Jack is thrice the sum of the ages of his two friends

Let The age of first friend = y years

Let The age of second friend = z year

So, sum of friend age = ( y + z ) years

A/C to statement

Age of Jack = 3 ×  ( y + z )

i.e   x = 3 y + 3 z                 .........1

Statement II

5 years hence Jack age will be twice the sum of friends ages.

So, After 5 years

Jack age = ( x + 5 ) years

age of first friend = ( y + 5 ) years

age of second friend = ( z + 5 ) year

So, sum of friend age = ( y + z +10 ) years

A/C to statement

Age of Jack = 2 ×  ( y + z + 10 )

i.e   x + 5 = 2 y + 2 z + 20                

Or,  x = 2 y + 2 z + 15              .........2

Solving eq 1 and 2

i.e  3 y + 3 z = 2 y + 2 z + 15              

Or, 3 y - 2 y + 3 z - 2 z = 15

Or, y + z = 15 years

So, The sum of friend's age = y + z = 15 years

from eq 1

x = 3 ( y +  z )

Put the value of y + z in eq 1

∴, x = 3 × 15 = 45 years

So, The Age of Jack = x = 45 years

Hence, The present Age of Jack is 45 years  . Answer