My two digit number is special because adding the sum of its digits
to the product of its digits gives me my original number. What
could my number be?
Think of a number... follow the machine's instructions. I know what
your number is! Can you explain how I know?
Learn to write procedures and build them into Logo programs. Learn to use variables.
Let the number of cases solved in 2003 be $x$. This was $80\%$ of the number of cases, so there were $5x/4$ cases to solve in 2003. So the number of cases to solve in 2004 was $5x/4 \times 6/5$, which is $3x/2$. Inspector Remorse solved $60\%$ of the cases, which is $9x/10$. So there was a $10\%$ decrease in the number of cases solved.
This problem is taken from the UKMT Mathematical Challenges.