rocio le dice a ana yo tengo el triple de años que tu tenias cuando yo tenia la mitad de la edad que tu tienes. y cuando tu tengas la edad que yo tengo nuestras eades sumaran 90 años. que edad tiene ana?

Answer: The age of Ana is 37.9 years old.

Explanation:

This can be translated to:

"Rocio tells Ana:

I have the triple of the age that you had when i had half your age.

And when you have the age that i have today, our ages will ad up to 90"

If A is the age of Ana, and R the age of Rocio, we have that:

when Rocio had half the age of Ana was k years ago

k years ago the age of Ana was A - k

R - k = A/2

R = 3 * (A - k)

Ana will have the age of Rocio in h years

A + h = R

in h years, Rocio will have R + h years.

A + h + R + h = R + R + h = 90

So we have 4 equations and 4 variables.

R - k = A/2

R = 3 * (A - k)

A + h = R

2R + h = 90

We can replace the third equation into the other 3.

(A + h) - k = A/2

(A + h) = 3 * (A - k)

2 * (A + h) + h = 90

Now we can isolate k from the first equation, and then replace it into the second equation:

A + h - k = A/2

k = A - A/2 + h = A/2 + h

and the second equation is:

(A + h) = 3 * (A - k) = 3 * (A - A/2 - h) = 3 * (A/2 - h)

Now we have two equations:

(A + h) = 3 * (A/2 - h)

2 (A + h) + h = 90

now we need to isolate h in one equation and replace it into the other, let's isolate h in the second equation:

2 (A + h) + h = 90

2A + 3h = 90

3h = 90 - 2A

h = 30 - (2/3) * A

now we replace it into the other equation:

(A + 30 - (2/3) * A) = 3 * (A/2 - 30 + (2/3) * A)

Now we solve this equation for A.

(1/3) * A + 30 = 3 * ((3/6) * A - 30 + (4/6) * A) = 3 * ((7/6) * A - 30)

(1/3) * A + 30 = (7/2) * A - 90

A * (7/2 - 1/3) = 30 + 90 = 120

A = 120 / (7/2 - 1/3) = 37.9