Problem 20 · 2009 Math Kangaroo
Stretch
Algebra & Patterns
work-backwardarithmetic-sequence
Meta collects pictures of famous sports people. Each year she collects as many pictures as she did in the previous two years. In 2008 she had 60 photos and this year she has 96. How many photos did she have in 2006?
Show answer
Answer: B — 24
Show hints
Hint 1 of 2
Each year's count equals the previous two years added together.
Still stuck? Show hint 2 →
Hint 2 of 2
You know 2008 and 2009; work backwards to find 2007, then 2006.
Show solution
Approach: reverse the 'sum of previous two' rule
- 2009 = 2008 + 2007, so 96 = 60 + (2007), giving 2007 = 36.
- 2008 = 2007 + 2006, so 60 = 36 + (2006).
- Then 2006 = 60 − 36 = 24.
- She had 24 photos in 2006.
Mark:
· log in to save