# Esther is three times as old as her sister janet. If the sum of their ages is 20 years old, what is the difference between their ages? it is a math question

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Let,

x - age of Esther and

y - age of Janet

Then, let's express the given conditions in math form.

For the first condition, Esther (x) is three times as old as Janet (y).

`x=3y`

For the second condition, the sum of their ages is 20. So we have,

`x+y=20`

Substitute x=3y.

`3y+y=20`

`4y=20`

`y=5`

Then, substitute value of y to x=3y.

`x=3*5`

`x=15`

So, Esther is 15 years old and her sister Janet is 5 years old.

Knowing their age, let's solve their age difference.

`x-y=15-5=10`

**Hence, the difference between their ages is 10 years.**

let x be the age of janet, then ester age will be 3x

According to question

x+3x=20

4x=20

x=5

therefore,janet age is 5 years old while his brother is 3x5=15 years old.

so,as per the question difference between their ages is

15-5=10 years old