age question

Question

Mr. Kim age is four times his son's. Six years ago, Mr. Kim was ten times as old as his son. How old are they both now.

Answer 1

Let k is Kim's age now.

Then, 6 yeas ago, Kim's age was (k-6).

 

Let s is her son's age now.

Then, 6 years ago, her son's age was (s-6).

 

We write an equation about

Mr. Kim age is four times his son's

     k = 4s ............................ (1)

 

We write a second relationship about

Six years ago, Mr. Kim was ten times as old as his son

                          (k-6) = 10(s-6)

          

We replace Mr Kim's age with its equivalent from (1) and solve the equation for s:

 

4s - 6 = 10(s-6)

4s -6 = 10s - 60

4s - 6 + 60 = 10s

4s +54 = 10s

54 = 10s - 4s

54 = 6s

s = 9.

Mr Kim's son is 9 years old.

Mr Kim is 36 years old.

 

6 years ago, Mr Kim's son was 3 years old.

6 years ago, Mr Kim was 30 years old.