Grades 11-12 Video Solutions 2011-11&12 Video Solutions 2011 problem2

Video Transcription

Question number 2. One year ago Luke was 10 years older than his sister. In 4 years he will be twice her age. How old is Luke? Let's set up some equations. Let L be Luke's age  and let S be his sister's age. One year ago Luke's age was given by L-1 and his sister's age was S-1 but he was already at that time 10 years older so we have the equation like  so. We have to add 10 to the sister's age and then we know that in 4 years Luke's age will be L-4 so we'll be his sister's but at that time he will be twice her age. So we  have the following 2 equations and 2 unknowns and we can solve. So what we can do here  in equation 1 is add 1 to both sides and we see that L is S plus 10 and then we will substitute  for L in the second equation. So we have L is equal to S plus 10 and then plus 4 and that's 2S plus 8 and this allows us to solve for S. In the left hand side we have S plus 14,  on the right hand side a 2S plus 8 so subtracting 8 from both sides and subtracting S from both  sides we see that S is equal to 6 and that's the sister's age and since L is S plus 10 Luke has to be 16 years old so the answer is B.

Video Summary

The problem involves determining Luke's current age based on his relationship with his sister's age. One year ago, Luke was 10 years older than his sister. In four years, Luke will be twice his sister’s age. Setting up equations, if L is Luke's age and S is his sister's, we find from the information given that L = S + 10. Substituting and solving these equations, we find that the sister’s current age, S, is 6 years old, making Luke 16 years old. Therefore, the answer is that Luke is currently 16 years old.

Keywords

Luke's age

sister's age

age relationship

equations

age problem