angela is 34 years old and jessica is 22 years old. How many years ago was angela 4 times as old as jessica

Question

angela is 34 years old and jessica is 22 years old. How many years ago was angela 4 times as old as jessica

Answer 1

We can represent Angela's age as a, and Jessica's as j. We know that Angela will always be 12 years older than Jessica (34-22 = 12). We want to know when Angela was 4 times as old as Jessica, i.e. when did a = 4*j. Since Angela is 12 years older, we can represent a as j+12 so a = j+12.

 

Now we want to know when did j+12 = 4*j. We want j to be one side so we'll subtract 1*j from both sides giving

12 = 3*j. Now we'll divide by 3 on both sides giving

4 = j. This tells us that when Jessica was 4, Angela was 16, which is both 4 times Jessica's age at that time and 12 more than Jessica's age. Since Jessica is 22 years old now we know that she was 4 years old, 18 years ago (22-4 = 18).