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:

Concept 1: Fraction

  • 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.

Concept 2: Ratio

  • 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).

Concept 3: Time

  • 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

Concept 3: Time 1

  • 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

Equation

Bar Model: Ethan's age now


So, how old is Ethan now?

Ethan is 15 years old now!

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