Question posted by Johnny from country unknown:
Ann is 12 years old. Her mother is 3 times as old as Ann. How many years ago was her mother 4 times as old as Ann?
Step 1: This is a question involving the Constant Difference Concept. It can be easily solved using the Model Method from Singapore Math. In these types of questions, the difference between the two variables given is always a constant. In this particular question, the constant difference is the age difference between Ann and her mother.
Ann's age = 12 years
Mother's age = 3 X 12 years = 36 years
Age difference = 36 years - 12 years = 24 years
Thus, the age difference between the two of them will always be 24 years.
We can then draw a box to represent Ann's age and 4 identical boxes to represent her mother's age since we want to find out how many years ago was her mother 4 times as old as her.
Step 2: Next, we can label the part of the model which represents their age difference, i.e., the three extra boxes that her mother has.
From the model,
3 units ----------> 24 years
1 unit ----------> 24 years / 3 = 8 years
Thus, Ann's mother was 4 times as old as her when Ann was 8 years old.
12 years - 8 years = 4 years
Therefore, Ann's mother was 4 times as old as her 4 years ago.