a girl is 6 years younger than her brother ,the prodict of their ages is 135.find their ages
(b - 6) * b= 135
b^2 - 6 b - 135 = 0
(b-15)(b+9) = 0
brother is 15.
15 - 6 = 9
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A girl is 6 years younger than her brother. The product of their ages is 135. Find their ages.
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To find the ages of the girl and her brother, we can form two equations based on the given information.
Let's assume the girl's age is represented by "x" and her brother's age is represented by "y".
According to the first piece of information, "a girl is 6 years younger than her brother," we can write the equation:
x = y - 6
Now, based on the second piece of information, "the product of their ages is 135," we can write another equation:
x * y = 135
We have two equations:
1) x = y - 6
2) x * y = 135
To solve these equations, we can substitute the value of x from the first equation into the second equation:
(y - 6) * y = 135
Expanding the equation gives us:
y^2 - 6y = 135
Rearranging the equation brings it into standard quadratic form:
y^2 - 6y - 135 = 0
Now, we can factorize this quadratic equation:
(y - 15)(y + 9) = 0
Setting each factor to zero gives us two possibilities:
y - 15 = 0 or y + 9 = 0
Solving these equations, we find:
y = 15 or y = -9
Since age cannot be negative, we discard y = -9.
So, the brother's age is 15. We can substitute this value into the first equation to find the girl's age:
x = y - 6
x = 15 - 6
x = 9
Therefore, the girl is 9 years old and her brother is 15 years old.