Age Ratio Problem: Solve for First Daughter's Age Using 2x and 5x Relationships

Mariana has 3 daughters.

The first daughter is 2 times older than the second daughter.

The second daughter is 5 times older than the third daughter.

If we increase the age of the third daughter by 12 years, she will be the same age as the second daughter.

How old is the the first daughter?

In the first step, we will try to use variables to change the exercise from verbal to algebraic.

Let's start with the third daughter and define her age as X.

The second daughter, as written, is 5 times older than her, so we will define her age as 5X.

The first daughter is 2 times older than the second daughter, so we will define her age as 2*5X, that is, 10X.

Now let's look at the other piece of information: it is known that if we increase the age of the third daughter by 12 years, then she will be the same age as the second sister.

So we will write X+12 (the third daughter plus another 12 years)

=

5X (age of the second daughter)

X + 12 = 5X

Once we have an equation, we can solve it. First, we'll move the sections:

5X-X=12

4X=12

We divide by 4:

X=3

But this is not the solution!

Remember, we were asked for the age of the first daughter, which is 10X

We replace the X we found:

10*3 = 30

This is the solution!