# Bar Model: What’s Ethan’s age?

Ethan is $\frac{1}{3}$ as old as his aunt now.

The ratio of Ethan’s age to his aunt’s age was 1 : 7 ten years ago.

How old is Ethan now?

Below are the related concepts to solve this question:

• Ethan is 1 part out of 3 parts of his aunt (Size of parts are relative to each other)
• The bar model parts of Ethan and his aunt’s now are longer than the bar model parts of them 10 years ago.
• The longer length indicates the addition of years from 10 years ago to now.

• Ethan is 1 part out of 7 parts of his aunt (Size of parts are relative to each other)
• The bar model parts of Ethan and his aunt’s 10 years ago are shorter than the bar model parts of them now.
• The shorter length indicates the subtraction of years from now (10 years ago).

• The bar model parts of Ethan and his aunt’s 10 years ago are relative to each other.
• The bar model parts of Ethan and his aunt’s now are relative to each other

• Age difference between Ethan and his aunt remains constant throughout their lifetime.
• As such, 6 units difference between Ethan and his aunt 10 years ago has the same value as (2 units + 20) difference between Ethan and his aunt now.
• This form the equation, 6 units → 2 units + 20

So, how old is Ethan now?

Ethan is 15 years old now!

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