Question

Agatha is five times older than her son bob. three years ago she was nine times older. how old is agatha?

Answer 1

Write an equation system based on the problem
"Agatha is five times older than her son, Bob" could be written as:
  a = 5b.......(first equation)
"Three years ago, she was nine times older" could be written as:
  a - 3 = 9(b - 3)......(second equation)

Solve the equation system
To find the value of b, substitute 5b as a to the second equation
a - 3 = 9(b - 3)
5b - 3 = 9(b - 3)
5b - 3 = 9b - 27
5b - 9b = -27 + 3
-4b = -24
   b = -24/-4
   b = 6
Her son, Bob, is 6 years old

To find Agatha's age, substitute the value of b to the first equation
a = 5b
a = 5 × 6
a = 30
Agatha is 30 years old