A boy is 6yrs older than his sister the product of their ages is 135'
Nine years old
To find the ages of the boy and his sister, we need to set up an equation based on the given information.
Let's assume the age of the sister is represented by "x." According to the given information, the boy is 6 years older than his sister, so his age can be represented as "x + 6."
The product of their ages is 135, so we can write the equation as:
x * (x + 6) = 135
To solve this equation, we can follow these steps:
Step 1: Expand the equation:
x^2 + 6x = 135
Step 2: Rearrange the equation in standard form by subtracting 135 from both sides:
x^2 + 6x - 135 = 0
Step 3: Factorize the quadratic equation:
(x + 15)(x - 9) = 0
Step 4: Set each factor equal to zero and solve for x:
x + 15 = 0 or x - 9 = 0
Solving each equation:
x = -15 or x = 9
Since age cannot be negative, we discard x = -15.
Therefore, the sister is 9 years old. To find the boy's age, we can substitute the value of x back into the expression:
Boy's age = x + 6 = 9 + 6 = 15
So, the boy is 15 years old, and the sister is 9 years old.
x(x+6) = 135
Hmmm. 135 = 9*15, so ...
Sister is X yrs. old.
Boy is x+6 yrs. old.
x(x + 6) = 135.
x^2 + 6x - 135 = 0,
(x-9)(x+16) = 0,
x - 9 = 0, X = 9.
x + 16 = 0, X = -16.
Solution: X = 9. x+6 = 9+6 = 15.