P7. This is an old problem but it is still fascinating.

One day three men went to a hotel and were charged $300 for their room. The desk clerk then realized that he had overcharged them $50 and he sent the refund up with the bellboy. Now the bellboy, being an amateur mathematician, realized that it would be difficult to split the $50 three ways. Therefore, he kept a $20 "tip" and gave the men only $30. Each man had originally paid $100 and was returned $10. Thus it cost each man $90 for the room. This means that they spent $270 for the room plus the $20 "tip," for a total of $290. What happened to the other $10?

P8. At a certain hamburger stand, the owner sold soft drinks out of two 16-gallon barrels. At the end of the first day, she wished to increase her profit, so she filled the soft-drink barrels with water, thus diluting the drink served. She repeated the procedure at the end of the second and third days. At the end of the fourth day, she had 10 gallons remaining in the barrels, but they contained only 1 pint of pure soft drink. How much pure soft drink was served in the four days?