A girl is six years younger than her brother, the product of their ages is 135.find their ages
2+6/5+3
To find the ages of the girl and her brother, we can set up a system of equations based on the given information.
Let's assume that the girl's age is represented by G, and her brother's age is represented by B.
From the given information, we can establish two equations:
1. The girl is six years younger than her brother: G = B - 6
2. The product of their ages is 135: G * B = 135
We can substitute the value of G from equation 1 into equation 2:
(B - 6) * B = 135
Expanding the equation, we get:
B^2 - 6B = 135
Rearranging the equation, we have:
B^2 - 6B - 135 = 0
Now, we need to solve this quadratic equation for B, the brother's age. We can factorize the equation or use the quadratic formula to find the values of B.
Factoring the equation, we get:
(B - 15)(B + 9) = 0
Setting each factor to zero, we have two possible values for B:
B - 15 = 0 --> B = 15
B + 9 = 0 --> B = -9
Since age cannot be negative, we discard the solution B = -9.
Therefore, the brother's age, B, is 15 years.
Now, substituting this value back into equation 1, we can find the girl's age, G:
G = B - 6
G = 15 - 6
G = 9
Hence, the girl's age is 9 years, and the brother's age is 15 years.
g = b - 6
g * b = 135
substituting ... (b - 6) * b = 135 ... b^2 - 6 b - 135 = 0
factoring ... (b + 9)(b - 15) = 0