# In eight years, Jack will be 2/3 as old as Tom. Four years ago he was 1/3 as old as Tom. Find their presentages (use 2 variables)Use the format “Given, Required, Solution, Checking, Final Answer”

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### 2 Answers

Given.

Let Jacks age be J and Tom's age be T.

In at years Jack will be (2/3) age of Tom.

4 years ago, Jack was 1/3 age of Tom.

Required:

Find the percentage between their ages NOW.

Solution.

Jacks age now is J, In 8 years his age will be J+8.

Tom's age now is T in 8 years years he will be T+8

==> (j+8) is (2/3) of (T+8)

==> j+8 = (2/3) (T+8)

==> J +8 = (2/3)T + 16/3

==> 3(j+8)= 2T+16

==> 3j +24 = 2T +16

==> 3J -2T = -8...........(1)

Four years ago (J-4) was 1/3 of (T-4)

==> J-4 = (1/3) (T-4)

==> 3J -12 = T-4

==> 3J-T = 8..............(2)

Now we will subtract (1) from (2).

==> **T = 16**

==> 3J -T = 8 ==> 3J -16 = 8==> 3J = 24 ==> J = 24/3 = 8

==> **J = 8**

Now we will find the percentage between their ages now.

==> J/T = 8/16 = 1/2

**Then, jack's now is half (1/2) as old as Tom.**

Let Jack's age 4 years ago be j and Tom's (4 years ago) be t.

Then, t = 3j

Thus,

j+4+8 = 2/3 (3j+4+8)

j+12=2/3 (3j+12)

3j+36 = 6j+24

3j=12

j=4

Thus, Jack is now 8 and Tom is 16.