- There are less than 40 members of the Landowners Association. These memebers vote on various proposals. All the members were present at a meeting and all voted on each of two proposals. On the first proposal 4 times as many memebers voted yes to those who voted no, On the second proposal 6 times as many voted yse as voted no. How many members are there?

-Four students tried to find the sum of the first 21 positive prime numbers. Bob got 709, Ned got 711, Matt got 712, and Lee got 713. Who was correct?

-The stegosaurus was 30 feet in length, weighed about 3500 pounds and had a brain that weighed only 3 ounces. An adult human male weighing 175 pounds has a brain weighing about 3 pounds. The ratio brain-weight/total-weight of a human is about _______ times greater than that of a stegosaurus.

- Joe is reading a book that needed 795 digits to number the pages. If the book started on page 1, how many pages are there in the book Joe is reading?

The second one:

2+3+5+7+11+13+17+19+23+29+31+37+41+43+47+53+59+61+67+71+73=712
Matt

The fourth one:
2-9=8 digits
10-99=178 digits
100-200=300 digits
201-300=297 digits
301=3 digits
302=3 digits
303=3 digits
304= 3 digits
8+178+300+297+12= 795
304 pages

I am confused, why did you not count the page one? Can you explain?

To find the number of members in the Landowners Association, we can solve the problem by setting up equations using the given information. Let's denote the total number of members as N.

1. Since all members were present at the meeting and voted on each of the two proposals, we can use the information given about the voting results.

- On the first proposal, 4 times as many members voted yes as voted no. This means the number of members who voted yes is 4 times the number who voted no: 4x = (N - x), where x represents the number of members who voted no.
- On the second proposal, 6 times as many members voted yes as voted no. This means the number of members who voted yes is 6 times the number who voted no: 6y = (N - y), where y represents the number of members who voted no.

We can solve these equations simultaneously to find the values of x and y, and then substitute them in any one of the equations to calculate the total number of members (N).

2. To determine who calculated the correct sum of the first 21 positive prime numbers, we can analyze the possible errors made by each student.

- Bob got 709: We can check if this is the correct sum by calculating the sum of the first 21 primes manually.
- Ned got 711: Similarly, we can check if this sum is correct.
- Matt got 712: We can verify the sum again.
- Lee got 713: We can verify the sum one more time.

By comparing the calculated sums with the given results, we can determine which student made the correct calculation.

3. To find the ratio of brain weight to total weight for a human compared to a stegosaurus, we need to calculate both ratios.

- For a human, the ratio is brain weight (3 pounds) divided by total weight (175 pounds).
- For a stegosaurus, the ratio is brain weight (3 ounces) divided by total weight (3500 pounds).

By converting both weights to the same unit (either pounds or ounces), we can compare the two ratios and find the ratio of the human brain-weight/total-weight to the stegosaurus brain-weight/total-weight.

4. To determine the number of pages in the book Joe is reading, we can use the fact that it took 795 digits to number the pages.

- Assuming each page number takes up one digit, we can find the maximum number of pages by considering the largest possible number of digits.
- If the book starts on page 1, the maximum number of pages is 999 (since the numbering uses 3 digits).
- We can iterate through possible numbers of pages, starting from 1, to find the smallest number where the number of digits exceeds 795. That will be the number of pages in the book Joe is reading.

Remember, the process explained above provides a step-by-step guide on how to approach each problem and find the solutions.