In three more 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?
Answers
Let
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)
Answer:
Miguel's present age is 11 yrs, and his grandfather's age is 57 yrs.
Step-by-step explanation:
Let present age of Miguel's = x yrs.
According to problem,
Sum of Miguel's and his grandfather's present age is 68 yrs.
His grandfather's present age = (68 - x) yrs.
In 3 yrs. more,
His grandfather's age = (68 - x ) + 3 =(71 - x) yrs.
Miguel's age 1 yr. before = (x - 1) yrs.
By the problem,
6 ( x - 1) = 71 - x
6x - 6 = 71 - x
6x+ x = 71 + 6
7x =77
x = 77/ 7= 11 yrs
His grandfather's present age = 68 - 11 =57 yrs.