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?
Vincent, you expect us to do a lot of problems for you
We call that homework dumping.
Before I do any more, tell me where your problem lies, or show me your preliminary steps.
57 +11-68
To solve this problem, we can use algebraic equations. Let's represent Miguel's present age as M and his grandfather's present age as G.
According to the problem, in three more years, Miguel's grandfather will be six times as old as Miguel was last year. This can be written as:
G + 3 = 6(M - 1)
Next, we are given that the sum of Miguel's present age and his grandfather's present age is 68:
M + G = 68
Now we have two equations with two unknowns, M and G. We can solve this system of equations using substitution or elimination.
Let's solve it using the substitution method:
First, we'll solve one equation for one variable (G in terms of M):
M + G = 68
G = 68 - M
Next, substitute G in the other equation:
G + 3 = 6(M - 1)
(68 - M) + 3 = 6(M - 1)
71 - M = 6M - 6
5M = 77
M = 15.4
Since age cannot be fractionary, we round M to the nearest whole number:
M = 15
Now substitute M = 15 back into one of the original equations to find G:
G = 68 - M
G = 68 - 15
G = 53
So currently, Miguel is 15 years old, and his grandfather is 53 years old.