Your cousin is 26 yr older than your sister. The product of their ages is 560. How old is your sister?
sister age = s
cousin age = c
c - s = 26
c s = 560 so c = 560/s
560/s - s - 26 = 0
560 - s^2 - 26 s = 0
s^2 + 26 s - 560 = 0
solution is a complex number, no real solution is possible.
To find out your sister's age, let's create equations based on the given information.
Let's assume your sister's age as "x" years. According to the information given, your cousin is 26 years older than your sister, so your cousin's age would be "x + 26" years.
The product of their ages is stated to be 560. So, we have the equation:
x * (x + 26) = 560
Now, let's solve this equation to find your sister's age.
x^2 + 26x = 560
Rearranging the equation:
x^2 + 26x - 560 = 0
Now, we have a quadratic equation. To solve this equation, we can factor it, complete the square, or use the quadratic formula. In this case, let's factor the equation:
(x - 10)(x + 56) = 0
Setting each factor equal to zero:
x - 10 = 0 or x + 56 = 0
Solving for x:
x = 10 or x = -56
Since we are dealing with ages, a negative age does not make sense in this context. Therefore, your sister's age is 10 years.