A woman is three years older than her sister and five years older than her brother .what is the total of their ages?
If the eldest sister's age is x, then the sum of their ages is
x + x-3 + x-5 = 3x-8
To find the total of their ages, we need to determine the ages of the sister and brother.
Let's assign variables to represent their ages:
- Sister's age: S
- Brother's age: B
Given that the woman is three years older than her sister and five years older than her brother, we can write two equations:
1. Woman's age = Sister's age + 3
2. Woman's age = Brother's age + 5
Since the woman's age is common to both equations, we can equate them:
S + 3 = B + 5
Now, we also know that the woman's age is the sum of the sister's age and 3, and also the sum of the brother's age and 5. Hence, we can write another equation:
Sister's age + 3 = Brother's age + 5
To solve this system of equations, we can substitute one equation into the other:
S + 3 = (S + 3) + 2
Simplifying the equation, we get:
S + 3 = S + 5
Now, we subtract S from both sides:
3 = 5
This is not a valid equation, which indicates that there is no solution. Therefore, we cannot determine the ages of the sister and brother, and as a result, we cannot find the total of their ages.