Sheena is now one third of her father's age.Twelve years hence she will be half as old as her father.Find their present ages??
Sheena's present age --- x
her dad's present age --- 3x
in 12 years:
Sheena's age = x+12
dad's age = 3x+12
x+12 = (1/2)(3x+12)
2x+24 = 3x + 12
x = 12
Shenna is pesently 12 and her dad is 36
Let's assume Sheena's father's age is "x" years.
According to the given information, Sheena is now one third of her father's age, so her current age is (1/3)x years.
Twelve years hence means after 12 years. So, Sheena's age after 12 years will be (1/3)x + 12 years.
According to the second piece of information, Sheena will be half her father's age after 12 years. So, we can set up the equation:
(1/3)x + 12 = (1/2)(x + 12)
Now, let's solve this equation step by step:
Multiply both sides of the equation by 6 to get rid of the fractions:
6 * [(1/3)x + 12] = 6 * [(1/2)(x + 12)]
2x + 72 = 3(x + 12)
Distribute 3 on the right side of the equation:
2x + 72 = 3x + 36
Subtract 2x from both sides of the equation:
2x - 2x + 72 = 3x - 2x + 36
72 = x + 36
Subtract 36 from both sides of the equation:
72 - 36 = x + 36 - 36
36 = x
Therefore, Sheena's father's age is 36 years, and Sheena's current age is (1/3) * 36 = 12 years.
So, their present ages are: Sheena is 12 years old, and her father is 36 years old.
To find the present ages of Sheena and her father, we can set up a system of equations based on the given information.
Let's assume Sheena's present age is S and her father's present age is F.
According to the first statement, "Sheena is now one third of her father's age":
S = (1/3)F ...(equation 1)
According to the second statement, "Twelve years hence she will be half as old as her father":
S + 12 = (1/2)(F + 12) ...(equation 2)
Now, we can solve this system of equations to find the values of S and F.
Substitute equation 1 into equation 2:
(1/3)F + 12 = (1/2)(F + 12)
Multiply both sides by 6 to eliminate the fractions:
2F + 72 = 3F + 36
Rearrange the equation:
3F - 2F = 72 - 36
F = 36
Substitute the value of F back into equation 1:
S = (1/3)(36)
S = 12
Therefore, Sheena's present age is 12 and her father's present age is 36.