In three more years, Sabrina's grandfather will be six times as old as Sabrina was last year. When Sabrina's present age is added to her grandfather's present age, the total is 68. How old is Sabrina now?
Let's denote Sabrina's current age as "S" years and her grandfather's current age as "G" years.
From the given information:
In three more years, Sabrina's grandfather will be six times as old as Sabrina was last year. This can be expressed as: (G + 3) = 6(S - 1)
When Sabrina's present age is added to her grandfather's present age, the total is 68. This can be expressed as: S + G = 68
Now, we have a system of two equations with two variables:
Equation 1: G + 3 = 6(S - 1) Equation 2: S + G = 68
Let's solve this system of equations using substitution. First, solve Equation 1 for G:
G = 6(S - 1) - 3
Now, substitute this expression for G into Equation 2:
S + (6(S - 1) - 3) = 68
Now, simplify and solve for S:
S + 6S - 6 - 3 = 68
7S - 9 = 68
7S = 68 + 9 7S = 77
S = 77 / 7 S = 11
So, Sabrina is currently 11 years old.
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