Question 514996: In 3 years, Miguel's grandfather will be six times as old as Miguel was last year. When Miguel's present age is added to his grandfather's present age, the total is 68. How old is each one now?
Answer by Maths68(1474)   (Show Source):
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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)
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