# 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

lemjay | Certified Educator

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.

rogal | Certified Educator

Esther is 3 times as old as Janet. Let Esther's age be x years old. Then Janet's age will be

\frac{1}{3} x .

The sum of their ages is 20, that is \frac{4}{3} x = 20 so that x = 20 \times \frac{3}{4} = 15

This means that Esther's age is 15 years, while Janet's age is 5 years.

The difference of their ages is: 15 - 5 = 10 years.





naz2011 | Student

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