A girl is 5years older than her brother, the product of their age is 54, find their age 1/2, 1/16, 1/8
age of brother --- x
age of girl ----- x+5
x(x+5) = 54
x^2 + 5x - 54 = 0
solve for x, reject the negative answer.
Was expecting a whole number solution, but did not get it.
Let's call the girl's age G and her brother's age B.
Given that the girl is 5 years older than her brother, we can write the equation:
G = B + 5 ...(Equation 1)
Also, we are given that the product of their ages is 54, which can be written as:
G * B = 54 ...(Equation 2)
Substituting Equation 1 into Equation 2, we get:
(B + 5) * B = 54
Expanding the equation:
B^2 + 5B = 54
Rearranging the equation to make it quadratic:
B^2 + 5B - 54 = 0
Now, let's solve the quadratic equation by factoring or using the quadratic formula:
(B + 9)(B - 6) = 0
Setting each factor equal to zero:
B + 9 = 0 or B - 6 = 0
Solving for B:
B = -9 or B = 6
We can disregard the negative value since age cannot be negative. Therefore, the brother's age (B) is 6.
Using Equation 1, we can substitute B with 6 to find the girl's age (G):
G = 6 + 5
G = 11
So, the girl is 11 years old and her brother is 6 years old.
Now, let's calculate the fractions you mentioned:
1/2 of the girl's age (G):
1/2 * 11 = 5.5
1/16 of the girl's age (G):
1/16 * 11 = 0.6875
1/8 of the brother's age (B):
1/8 * 6 = 0.75
Therefore, 1/2 of the girl's age is 5.5, 1/16 of the girl's age is 0.6875, and 1/8 of the brother's age is 0.75.
To find the ages of the girl and her brother, we can set up a system of equations using the information given.
Let's assume the brother's age is x. According to the given information, the girl is 5 years older, so her age would be x + 5.
The product of their ages is 54, so we have the equation:
x * (x + 5) = 54
Now, we can solve this equation to find the values of x and x + 5 which represent their ages.
To solve this quadratic equation, we can rearrange it and solve for x:
x^2 + 5x - 54 = 0
Now, we have a quadratic equation in the form ax^2 + bx + c = 0. We can solve it by factoring, completing the square, or using the quadratic formula.
Using the quadratic formula, which is x = (-b ± √(b^2 - 4ac))/(2a), we can substitute in our values:
x = (-5 ± √(5^2 - 4 * 1 * -54))/(2 * 1)
Simplifying further, we have:
x = (-5 ± √(25 + 216))/(2 * 1)
x = (-5 ± √(241))/(2)
Since we need to find their ages as fractions, we can approximate the square root of 241 to two decimal places as 15.52. Substituting it into the equation, we have:
x = (-5 ± 15.52)/(2)
We have two possible solutions:
1. When x = (-5 + 15.52)/(2) ≈ 5.26, the brother's age is approximately 5.26 years, and the girl's age would be approximately 10.26 years.
2. When x = (-5 - 15.52)/(2) ≈ -10.26 (discarded as ages cannot be negative), we disregard this solution.
Therefore, the possible ages are approximately 5.26 years for the brother and 10.26 years for the girl.
To find their ages as fractions, we can express them in simplest form:
The brother's age as 1/2 can be approximated as 5 1/4 years.
The brother's age as 1/16 can be approximated as 5 1/14 years.
The brother's age as 1/8 can be approximated as 5 1/8 years.
Similarly, the girl's age as 1/2 can be approximated as 10 1/4 years.
The girl's age as 1/16 can be approximated as 10 1/14 years.
The girl's age as 1/8 can be approximated as 10 1/8 years.
Please note that these are approximate values rounded to the nearest 1/4, 1/14, and 1/8.