A grandfather is ten times older than his granddaughter.he is also 54 years older than her. Find their present ages.
g = grandfathers age
d = granddaughter age
You have two conditions for a grandfather:
g = 10 d
g = d + 54
Now:
g = g
10 d = d + 54 Subtract d to both sides
10 d - d = d + 54 - d
9 d = 54 Divide both sides by 9
d = 54 / 9 = 6 yrs
g = 10 d = 10 * 6 = 60 yrs
OR
g = d + 54
g = 6 + 54 = 60 yrs
Their present ages:
grandfather 60 yrs
granddaughter 6 yrs
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To solve this problem, let's assign variables to represent the ages of the grandfather and the granddaughter. Let's call the grandfather's age G, and the granddaughter's age D.
According to the problem, the grandfather is ten times older than his granddaughter. This can be expressed as:
G = 10D ----(Equation 1)
It is also given that the grandfather is 54 years older than the granddaughter, which can be expressed as:
G = D + 54 ----(Equation 2)
Now we have a system of equations with two variables (G and D). We can solve this system of equations to find their ages.
To eliminate one of the variables, let's solve Equation 1 for D:
D = (1/10)G ----(Equation 3)
Now substitute this value of D into Equation 2:
G = (1/10)G + 54
Multiply both sides of the equation by 10 to get rid of the fraction:
10G = G + 540
Subtract G from both sides of the equation:
10G - G = 540
Combine like terms:
9G = 540
Divide both sides of the equation by 9:
G = 60
Now we know that the grandfather is 60 years old.
Substitute this value of G into Equation 3 to find D:
D = (1/10) * 60
D = 6
Therefore, the grandfather is currently 60 years old, and the granddaughter is currently 6 years old.