A student wants a real image of a candle flame, 2.5 times as tall as the flame, on a wall 105 cm…

Step 1. The signs. The image is real, so $v = -105\ \text{cm}$. It is real and enlarged, so $m = -2.5$.

Step 2. The candle. $m = -\dfrac{v}{u}$, so $u = -\dfrac{v}{m} = -\dfrac{-105\ \text{cm}}{-2.5} = -42\ \text{cm}$.

Step 3. The focal length. $\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u} = -\dfrac{1}{105\ \text{cm}} - \dfrac{1}{42\ \text{cm}} = -\dfrac{2 + 5}{210\ \text{cm}} = -\dfrac{1}{30\ \text{cm}}$, so $f = -30\ \text{cm}$.