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PrintSouth African Mathematics Olympiad Second Round
South Africa algebra
Problem
14. I accidentally decreased a number by instead of increasing it by . This incorrect value now needs to be increased by to get to the correct value. What is the value of ?
15. Exactly two years ago the Benson family had 4 members, and their average age was . The Bensons then adopted another child. If the average age of the family today is still , what is the present age of the adopted child?
15. Exactly two years ago the Benson family had 4 members, and their average age was . The Bensons then adopted another child. If the average age of the family today is still , what is the present age of the adopted child?
Solution
14. I ended up with of the number instead of . So I need to multiply this new result by , or add it three times to itself, which is an increase of .
15. 2 years ago the sum of all the family's ages was . That should have increased by , but has actually become , i.e. increased by . So the new person is now years old.
15. 2 years ago the sum of all the family's ages was . That should have increased by , but has actually become , i.e. increased by . So the new person is now years old.
Final answer
k = 300; adopted child's present age = 11
Techniques
Fractions