Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 4.3 AIME Find the answer South Africa

14. I accidentally decreased a number by $60\%$ instead of increasing it by $60\%$ . This incorrect value now needs to be increased by $k\%$ to get to the correct value. What is the value of $k$ ?

15. Exactly two years ago the Benson family had 4 members, and their average age was $19$ . The Bensons then adopted another child. If the average age of the family today is still $19$ , what is the present age of the adopted child?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

14. $300$
I ended up with $40\%$ of the number instead of $160\%$ . So I need to multiply this new result by $4$ , or add it three times to itself, which is an increase of $300\%$ .

15. $11$
2 years ago the sum of all the family's ages was $4 \times 19 = 76$ . That should have increased by $2 \times 4 = 8$ , but has actually become $5 \times 19 = 95$ , i.e. increased by $19$ . So the new person is now $19 - 8 = 11$ years old.

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