In three more years, Miguels grandfather will be six times as old as Miguel was last
year. When Miguels present age is added to his grandfathers present age, the total is 68.
How old is each one now?
11 years
12 years
10 years
15 years
Explanation:
Miguels present age be "m"
Grandfathers present age be "g"
Then m + g = 68
Miguels age "last year" was m – 1
His grandfathers age "in three more years" will be g + 3
The grandfathers "age three years from now" is six times Miguels "age last year"
i.e., g + 3 = 6(m – 1)
This gives me two equations with two variables:
m + g = 68
g + 3 = 6(m – 1)
Solving the first equation,
m = 68 – g
g + 3 = 6m – 6
g + 3 = 6(68 – g) – 6
g + 3 = 408 – 6g – 6
g + 3 = 402 – 6g
g + 6g = 402 – 3
7g = 399
g = 57
Since "g" stands for the grandfathers current age, then the grandfather is 57.
Since m + g = 68,
then m = 11
Miguel is presently eleven years old
Miguels present age be "m"
Grandfathers present age be "g"
Then m + g = 68
Miguels age "last year" was m – 1
His grandfathers age "in three more years" will be g + 3
The grandfathers "age three years from now" is six times Miguels "age last year"
i.e., g + 3 = 6(m – 1)
This gives me two equations with two variables:
m + g = 68
g + 3 = 6(m – 1)
Solving the first equation,
m = 68 – g
g + 3 = 6m – 6
g + 3 = 6(68 – g) – 6
g + 3 = 408 – 6g – 6
g + 3 = 402 – 6g
g + 6g = 402 – 3
7g = 399
g = 57
Since "g" stands for the grandfathers current age, then the grandfather is 57.
Since m + g = 68,
then m = 11
Miguel is presently eleven years old