Problem 6 · 2013 Math Kangaroo
Medium
Algebra & Patterns
substitution
Let f be a linear function for which \(f(2013) - f(2001) = 100\). What is the value of \(f(2031) - f(2013)\)?
Show answer
Answer: D — 150
Show hints
Hint 1 of 2
A linear function changes by the same amount over equal steps.
Still stuck? Show hint 2 →
Hint 2 of 2
Find the per-year change, then scale it to the new gap.
Show solution
Approach: constant slope of a linear function
- From 2001 to 2013 is 12 years and the change is 100, so the slope is 100/12.
- From 2013 to 2031 is 18 years.
- Change = 18 · (100/12) = 150, so D.
Mark:
· log in to save