IMC 2009 Q15
15. What is the value of \(\dfrac{1}{x + 2}\), given that \(\dfrac{1}{x} = 3.5\) ?
- A \(\dfrac{7}{9}\)
- B \(\dfrac{7}{16}\)
- C \(\dfrac{9}{7}\)
- D \(\dfrac{7}{4}\)
- E \(\dfrac{16}{7}\)
Intermediate Mathematical Challenge 2009, Question 15. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B \(\dfrac{7}{16}\)
As \(\dfrac{1}{x} = 3.5 = \dfrac{7}{2}\), \(x = \dfrac{2}{7}\). So \(x + 2 = \dfrac{16}{7}\). Hence \(\dfrac{1}{x + 2} = \dfrac{7}{16}\).
Solution © UK Mathematics Trust, from the IMC 2009 solutions.