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 Miguel and his grandfather now?
Miguel = 11
and his grandfather = 57
57 + 11 = 68
correct?
ahhh, found this in the Related Questions below
"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? "
Amazing what effect proper punctuation and correct usage of a period has on understanding of a problem.
let Miguel's present age be x
let grandpa's present age be y
y+3 = 6(x-1)
y+3 = 6x - 6 ---> y = 6x-9
x+y = 68
x + 6x-9 = 68
7x = 77
x = 11
then y = 66-9 = 57
Miguel is now 11 and his grandfather now is 57
could you do this question with on varible
To solve this problem, let's break it down step by step.
Let's assume Miguel's current age is "M" and his grandfather's current age is "G".
We know that in three more years, Miguel's grandfather will be six times as old as Miguel was. This can be represented by the equation: G + 3 = 6(M+3).
Next, we are given that last year, when Miguel's present age is added to his grandfather's present age, the total is 68. This can be represented by the equation: (M-1) + (G-1) = 68.
Now, we can solve these two equations simultaneously to find the values of M and G.
Equation 1: G + 3 = 6(M+3)
Equation 2: (M-1) + (G-1) = 68
Let's start with Equation 2:
(M-1) + (G-1) = 68
M + G - 2 = 68
M + G = 68 + 2
M + G = 70
Now, let's substitute this value of (M + G) into Equation 1:
G + 3 = 6(M+3)
G + 3 = 6M + 18
G = 6M + 18 - 3
G = 6M + 15
Substituting the value of (M + G) from Equation 2 into this equation:
M + G = 70
M + (6M + 15) = 70
7M + 15 = 70
7M = 70 - 15
7M = 55
M = 55/7
M ≈ 7.86
Since we are dealing with ages, we can assume that Miguel's age cannot be a fraction. Therefore, we can approximate it to the nearest whole number.
M ≈ 8
Now, substituting this value of M into Equation 2:
M + G = 70
8 + G = 70
G = 70 - 8
G = 62
So, Miguel is approximately 8 years old and his grandfather is approximately 62 years old.
The wording of your question makes no sense.
"In three more years, Miguel's grandfather will be six times as old as Miguel was."
--- was when ??
" Last year, when Miguel's present age is added to his grandfather's
present age the total is 68."
-- This makes no sense at all.
-- where does the "last year" enter the picture ?
Why is Miguel 11 years old?
Where did you get that from?
btw, your answers do not match the description.
e.g. in 3 more years his grandfather would be 60 which is not six times 11