A fruit seller sells 45% of the oranges that he has along with one more orange to a customer. He then sells 20% of the remaining oranges and 2 more oranges to a second customer. He then sells 90% of the now remaining oranges to a third customer and is still left with 5 oranges. How many oranges did the fruit seller have initially?

$$\eqalign{ & {\text{Let total numbe of oranges}} = x \cr & \left\{ {\left( {\frac{{x \times 55}}{{100}} - 1} \right) \times \frac{{80}}{{100}} - 2} \right\} \times \frac{{10}}{{100}} = 5 \cr & \left( {\frac{{x \times 55}}{{100}} - 1} \right) \times \frac{{80}}{{100}} = 50 + 2 \cr & \left( {\frac{{x \times 55}}{{100}} - 1} \right) = \frac{{52 \times 10}}{8} \cr & \frac{{x \times 55}}{{100}} - 1 = 65 \cr & \frac{{x \times 55}}{{100}} = 66 \cr & x = \frac{{66 \times 100}}{{55}} \cr & x = 120 \cr} $$