Sally is 54 years old and her mother is 80, how many years ago was Sally’s mother three times her age?

Question

Sally is 54 years old and her mother is 80, how many years ago was Sally’s mother three times her age?

Answer 1

Let us assume x years back , Sally's mom's age is 3 times of Sally's age. Hence

 

3(54-x) = 80-x

162-3x=80-x

162-80 = 3x-x

82=2x

x=41.

So , 41 years ago, Mothers age is 3 times of Sally's age.

 

When Sally's age was 13 (54-41), and her mom age was 39 (80-41).

Answer 2

First, how far apart in age are they?  80-54=26.  With that, you can set up your equation:

 

Mother = Sally + 26

M=S+26, or S=M-26

 

• M=3S when?
• M=3(M-26)
• M=3M-78
• 2M=78
• M=39

 

When Mom was 39, those conditions were met (Mom 39, Sally 39-26, or 13, and yes 39=3*13)

If Mom is 80 now, she was 39 41 years ago (80-39)