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?

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)

## 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)

JMa beer!