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The sum of Jack's age and Jill's ages is 18.

The sum of Jack's age and Jill's ages is 18. In 3 years, Jack will be twice as old as Jill.

What are their ages now?

Duration: 
expired

This is a typical age problem

This is a typical age problem that can be solved using systems of equations in 2 variables.

We will supply the following representations:

Let:
Now In 3 years
==============================
Jack | x | x + 3
==============================
Jill | y | y + 3
==============================

Given that the sum of their ages NOW is 18:

x + y = 18 (Eq. 1)

In 3 years, Jack will be twice as old as Jill. This means:

x + 3 = 2(y + 3) (Eq. 2)

Simplifying Eq 2 gives:

x + 3 = 2y + 6

Solving for x gives:

x = 2y + 6 - 3
x = 2y + 3 (Eq. 3)

Substituting Eq 3 to Eq 1 gives:

x + y = 18
(2y + 3) + y = 18
3y + 3 = 18
3y = 18 - 3
3y = 15
y = 15/3
y = 5

Substituting this value of y to Eq 1 gives:

x + y = 18
x + 5 = 18
x = 18 - 5
x = 13

Therefore, x = 13 and y = 5, or the age of Jack NOW is 13 and Jill is 5.

CHECK:
x + y = 18
13 + 5 = 18
18 = 18 (Check)

In 3 years:
13 + 3 = 16
5 + 3 = 8

Thus, 16 is twice 8. (Check)