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16 February, 12:20

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?

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  1. 16 February, 13:43
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    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
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