Monica is one-third as olf as her sister. six years hence she will be one-half as old as her sister find their present age

Direct method:

sister ---- x
Monica --- (1/3)x or x/3

6 years from now:
age of sister = x+6
Monica's age = x/3 + 6

x/3 + 6 = (1/2)(x+6)
multiply each term by 6, the LCD
2x + 36 = 3(x+6)
2x+36 = 3x + 18
18 = x

The sister is 18, and Monica is 6

or

sometimes fractions can be avoided by rephrasing the conditions:
if Monica is 1/3 her sister's age, then the sister is 3 times as old as Monica
let Monica's age be y
then sister's age is 3y

in 6 years, Monica will be y+6 and the sister 3y+6
At that time, Monica is half as old as the sister,
or
the sister is twice as old as Monica
3y+6 = 2(y+6)
3y + 6 = 2y+12
y = 6 , ---> 3y = 18

So Monica is 6, the sister is 18

Monica is one-third as old as her sister. Six years hence, she will be one-half as old as her sister. Find the present age of monica

To find Monica's present age, let's assume her age as x.

According to the given information, Monica is one-third as old as her sister. So, her sister's age would be 3x (three times Monica's age).

Now, let's find their ages after six years.

Monica's age after six years would be x + 6, and her sister's age after six years would be (3x) + 6.

According to the given information, six years hence, Monica will be one-half as old as her sister. So, we can write the following equation:

x + 6 = (1/2)((3x) + 6)

Now, let's solve the equation to find Monica's present age:

2(x + 6) = 3x + 6

2x + 12 = 3x + 6

Subtracting 2x from both sides, we get:

12 = x + 6

Subtracting 6 from both sides, we get:

6 = x

Therefore, Monica's present age is 6.

Since Monica is one-third as old as her sister, her sister's age would be 3 * 6 = 18.

Hence, Monica's present age is 6 years, and her sister's present age is 18 years.