Problem solving.
Please explain all your answers. State which problem solving strategy you are using. Sections 1.1 and 1.2 of the textbook may help.
1. In a target shooting game, Spencer had four arrows. He hit the target with all four shots. With each shot he could have scored 25 points, 10 points, 5 points, or 1 point. How many total scores are possible?
2. Juana threw five darts at a dartboard. The possible scores on the target were 2, 4, 6, 8, 10. Each dart hit the target. Which of these total scores can be quickly identifies as not possible: 38, 23, 58, 30, 42, 31, 26, 6, 14, or 15?
3. If the eggs in a basket are removed two at a time, one egg will remain. If the eggs are removed three at a time, two eggs will remain. If the eggs are removed four, five, or six at a time, then three, four, and five eggs will remain, respectively. But if they are taken out seven at a time, no eggs will be left over. Find the least number of eggs that could be in the basket.
4. To keep the spectators out of the line of flight at an air show, the ushers arranged the show’s seats in the shape of an inverted triangle. Kevin, who loves airplanes, arrived very early and was seated in the front row, which contained one seat. The second row contained three seats, and those filled very quickly. The third row contained five seats, which were given to the next five people who came. The next row contained seven seats. This seating pattern continues all the way to the last row, with each row containing two more seats than the previous row. All 20 rows were filled. How many people attended the air show?
5. What is the digit in the ones place of 257?