Question 65733: "How old are you?" Alex asked his cousin Gustav one day. "The day before yesterday," replied Gustav, "I was twice as old as my sister, but next year I will be three times as old as she is now." How old is Gustav? When is his birthday? On what day did this conversation take place? How old is Gustav's sister?
Found 2 solutions by venugopalramana, Edwin McCravy:
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! "How old are you?" Alex asked his cousin Gustav one day. "The day before yesterday," replied Gustav, "I was twice as old as my sister, but next year I will be three times as old as she is now." How old is Gustav? When is his birthday? On what day did this conversation take place? How old is Gustav's sister?
LET THE PRESENT AGE OF GUSTAV'S SISTER=X
PRESENT AGE OF GUSTAV=2X
NEXT YEAR AGE OF GUSTAV =2X+1 = 3X
X=1
GUSTAV'S PRESENT AGE = 2YRS.
CONVERSATION TOOK PLACE ON 1 DAYS AFTER GUSTAV'S BIRTH DAY
PRESENT AGE OF GUSTAV'S SISTER=1 YR.
Answer by Edwin McCravy(20054)  (Show Source):
You can put this solution on YOUR website! "How old are you?" Alex asked his cousin Gustav one day. "The day before
yesterday," replied Gustav, "I was twice as old as my sister, but next year I
will be three times as old as she is now." How old is Gustav? When is his
birthday? On what day did this conversation take place? How old is Gustav's
sister?
I have a different answer from Venugopalramana. I agree with Venugopalramana
that if Gustav was 2 and his sister 1, then he would turn 3 the next year.
However, if Gustav was only a 2-year old toddler, he couldn't be having that
kind of a conversation. So I claim he had to be a little bit older.
Two days before the conversation Alex was 4 and his sister was 2. That is twice
as old. Alex turned 5 some time between then and the end of that year. His
sister was still 2 on the day of the conversation. The next year Alex turned
6, and that is three times as old as the 2 years of age his sister was on the
day of the conversation.
There is no way to tell when Gustav's birthday is, nor what day the
conversation took place. All we can tell is that his 5th birthday was
later in the year than 2 days before the conversation took place, and that his
sister was 2 years old two days before the conversation and she was still 2 on
the day of the conversation.
Edwin
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