Question

15 years ago, a father was three times as old as his daughter. Now the father is only twice as old as his daughter. Find the
sum of the present ages of daughter and father.​

Answer 1

Answer:

Explanation:

Let the father's age be x and the daughter's age be y.

If the father's age was 3 times the daughter's age 15 years ago, then

x-15 = 3(y-15) (equation 1)

If the father's age now is twice the daughter's age now, then

x = 2y (equation 2)

Substitute equation 2 into equation 1:

2y-15 = 3(y-15)

2y-15 = 3y-45

2y -3y = -45 + 15

-y = -30

y = 30

Substitute y = 30 into equation 2 from above:

x = 2•30

= 60

.: The father is currently 60 years old and the daughter's current age is 30.

therefore, sum of their ages is 60 + 30 = 90

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Answer 2

Answer:

Sum of their ages is 90

Explanation:

For this question we are assuming the fathers age as x and daughter's age as y.

According to the question -

Father is 3 times the daughter's age.

then,

we can say -

x-15 = 3(y-15) -------- take it as equation 1

another situation according to the question is -

Age of father is twice of daughter's age.

Then,

we can say -

x = 2y ---------- take it as second equation

using Substitution method, put equation 2 into equation 1,

accordingly-

2y - 15 = 3(y - 15)

2y - 15 = 3y - 45

45-15 = 3y-2y

30 = y

or

y = 30

Lets substitute value of y into equation 2

Then,

x = 2x30 = 60

Therefore, the father's age is 60 years old and the daughter's age is 30.

And the sum of their ages is 60 + 30 = 90