One-half of Heather's age two years from now plus one-third of her age three years ago is twenty years. How old is she now?

• Present age of Miguel = m
  Present age of grandfather = f
  
  
  
  When Miguel's present age is added to his grandfather's present age, the total is 68
  f+m=68
  f=68-m...............(1)
  In 3 years,
  grand father present age = f+3
  Miguel was last year = m-1
  In 3 years, Miguel's grandfather will be six times as old as Miguel was last year Miguel's grandfather will be six times as old as.
  f+3=6(m-1)
  f+3=6m-6
  f=6m-6-3
  f=6m-9...........(2)
  
  Put the value of f from (1) to (2)
  68-m=6m-9
  -m-6m=-9-68
  -7m=-77
  Divide by -7 both sides
  -7m/-7=-77/-7
  m=11
  Put the value of m in (1)
  f=68-m
  f=68-11
  f=57
  
  Present age of Miguel = m = 11
  Present age of grandfather = f = 57
  Check
  Sum of their ages = 11+57 = 68
  Last year Miguel was = 11-1 = 10
  In three years Grandfather will be = 57+3 = 60 (which is 6 times of 10)
  
  
• 9 years agoHelpfull: Yes(0) No(1)