Travis is 19 years older than his sister Danielle. In 14 years, he will be twice as old as Danielle. How old is each of them now

Let's solve this step-by-step:

Step 1: Assign variables.
Let's assign variables to the ages of Travis and Danielle.
Let T = Travis's age
Let D = Danielle's age

Step 2: Translate the given information into equations.
We're given two pieces of information:
1. Travis is 19 years older than Danielle. This can be expressed as: T = D + 19.
2. In 14 years, Travis will be twice as old as Danielle. This can be expressed as: (T + 14) = 2(D + 14).

Step 3: Solve the equations.
Using the first equation, we can substitute for T in the second equation:
(D + 19 + 14) = 2(D + 14).

Simplifying, we get: D + 33 = 2D + 28.

Subtracting D from both sides, we get: 33 = D + 28.

Subtracting 28 from both sides, we get: 5 = D.

Step 4: Calculate the ages.
Now that we have the value of Danielle's age (D = 5), we can substitute it back into the first equation to find Travis's age:
T = D + 19
T = 5 + 19
T = 24.

Therefore, Danielle is 5 years old and Travis is 24 years old.

To determine the current ages of Travis and Danielle, we can set up a system of equations based on the given information.

Let's assume Danielle's current age is "D" years.

According to the information provided, Travis is 19 years older than Danielle, so his current age can be expressed as "D + 19".

In 14 years, Travis will be "D + 19 + 14" years old, and Danielle will be "D + 14" years old.

We are also told that in 14 years, Travis will be twice as old as Danielle. Mathematically, we can represent this as:

D + 19 + 14 = 2 * (D + 14)

Let's solve this equation to determine the value of D.

D + 33 = 2D + 28

Subtracting D from both sides:

33 = D + 28

Subtracting 28 from both sides:

5 = D

Therefore, Danielle's current age (D) is 5 years.

Since Travis is 19 years older than Danielle, his current age is:

D + 19 = 5 + 19 = 24 years.

So, Danielle is currently 5 years old, and Travis is currently 24 years old.

Danielle's age ---- x

Travis' age ------ x+19

14 years from now:
Danielle ------- x + 14
Travis ---------- x+19 + 14 = x+33

x+33 = 2(x+14)

take over, it is easy from there.