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?

The boys ages cannot be determined, but we know that the shells were divided in the proportions of 9:12:14. The youngest boy got 198, the next oldest got 264, and the oldest got 308.

172. If 30 baseballs are needed for 9 pitchers over 2 days of practice, what is the number of baseballs needed for 11 pitchers over 3 days of practice?

55. Here is a proportion that solves the problem: Let x = the unknown number of baseballs 30/9x2 = x/11x3 5/3 = x/33 3x = 165 x = 55.

173. Using the numbers 1, 9, 9 and 9, in that order, make the number 89. You
may use brackets and any standard math operation such as the square root, +, -, * and /. For example, 26 = -1 + 9 + 9 + 9.

174. What is the number which is 4 times the number that is one-eighth of one-tenth of one-half of 640?

16. (640 ÷ 2 = 320 ÷ 10 = 32 ÷ 8 = 4 X 4 = 16).

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.

42 inches. Use of simple geometry reveals that the answer to this problem is obtained by multiplying together the heights of the two poles, and then dividing this by the sum of the poles heights. Thus, 78 X 91 divided by 78 + 91.

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?

179. Statistics show that six out of ten major league baseball players will have a
batting average of 0.270 or better. What are the odds that a major leaguer will hit at least 0.270?

2 to 3. The probability of not hitting 0.270 or better is 4/10. The probability of hitting 0.270 or better is 6/10. Then, 4/10 divided by 6/10 = 4/6 = 2/3. So the odds are 2 to 3 that any major leaguer will hit 0.270 or better.

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?

Each widget costs $1.05 and the package is $.05.