Age question

Question

Time is one third as old as his grandpa.  Eigth year ago, four times Tim’s age was six more than grandpas age. How old were they

Answer 1

Assume T is Tim’s current age and G is grandpa’s current age. Then we can write:

 

T=G/3.  {Or T=(1/3)*G, Or 3*T=G}

 

eight years ago Tims age was T-8 and grandpa’s was G-8, so the second part of the problem can be written as:

(4*(T-8))=(G-8)+6    After simplification: 4*T-32=G-2 or 4*T-30=G

then we can set the following system of equations

G=3*T

G=4*T-30

so Tim is 30 years old now amd his grandpa is 90 years old. Eight years ago Tim was 22, and grandpa was 82 (4*22-6=82)!

 

Answer 2

 T is Tim's age now

G is the grandfather's age now

 

 

8 years ago....

4(T-8) = (G-8) + 6

4T - 32 = G -2

4T - 30= G

 

Currently, G = 3T <--- Tim is 1/3 as old as the grandfather, which is the same as saying grandfather is 3 times as old

 

4T - 30= 3T

 

4T - 30 - 3T = 0

 

T - 30 = 0

 

T = 30

 

Tim is 30. Grandfather is 90.

Eight years ago, Tim was 22 and grandfather was 82.

 

4(22) - 6 = 88 - 6 = 82 <--- yes, 4 times Tim's age, less 6 is grandfather's age.

                                            the answers are correct!

 

Tim is currently 30, and grandfather is 90.

Eight years ago, they were 22 and 82 respectively.