171. After collecting 770 shells, the three boys divided them up so that their amounts were in the same proportions as their ages. As often as Mike took four shells, Nick took three, and for every six that Mike received, Sam took seven. How many shells did each boy get?
175. A knight in the Middles Ages is talking with a king. The knight says, "if you give me five of your shields, I will have twice as many shields as you. If I give you two of my shields, I will have one quarter as many shields as you." How many shields do the knight and the king each have to begin with?
176. A man planted 2 poles upright in level ground. One pole was 6ft. 6in. and the other was 7ft. 7in. above ground. From the top of each pole he tied a string to the bottom of the other pole, just where it entered the ground. What height above the ground was the point where the two strings crossed? It is of no consequence as to how far apart the poles are. Two feet or two hundred feet, it will not affect the answer.
177. Find the six-digit number in which the first and last digits are the same; the first and last digits multiplied by two gives a two-digit number, now the second and third digits; and the last digit multiplied by three gives a two-digit number, now the fourth and fifth digits. The sum of all the digits is 22.
178. While visiting a Junior High School, I asked two students to give me their ages. The did so, and then, to test their arithmetical powers, I asked each of them to add the two ages together. One game me 44 as the answer, and the other gave me 1280. I immediately saw that one of them had subtracted one age from the other, while the other student had multiplied the two ages together. Can you tell what the students ages were?
180. You are working on some estimates for your boss. You can come up with a very good package for your new little widgets, but the packaging may be too expensive. The cost of the widget and the packaging is $1.10, and the widget is $1.00 more than the package. How much will you tell the boss that the package for each widget will cost?