Let's solve this step by step. We have a sister and brother where the sister is 3 years older. We need to find their current ages given that in 20 years their combined age will be 100. Let's define S as the sister's current age and B as the brother's current age.
Now let's set up our equations. First, since the sister is 3 years older than the brother, we have S equals B plus 3. Second, in 20 years their combined age will be 100, so S plus 20 plus B plus 20 equals 100. We can simplify this to S plus B plus 40 equals 100, which gives us S plus B equals 60.
Now we solve the system of equations. We have S equals B plus 3, and S plus B equals 60. Let's substitute the first equation into the second. We get B plus 3 plus B equals 60, which simplifies to 2B plus 3 equals 60. Subtracting 3 from both sides gives us 2B equals 57, so B equals 28.5.
Now we can find the sister's age. We know that B equals 28.5, and we have the equation S equals B plus 3. Substituting the value of B, we get S equals 28.5 plus 3, which equals 31.5. Therefore, the sister is currently 31.5 years old.
Let's verify our answer. Currently, the sister is 31.5 years old and the brother is 28.5 years old. The age difference is 31.5 minus 28.5 equals 3, which matches the problem statement. In 20 years, they will be 51.5 and 48.5 years old respectively, and their combined age will be 51.5 plus 48.5 equals 100, which also matches. Therefore, the sister's current age is 31.5 years.