Twelve winners in October Math Mania

1. The number of hours that were left in the day was one-third of the number of hours that had already passed. How many hours were left in the day?

Answer: 6 hours. One suggestion for solving this problem is to write and solve an equation.

Let h represent the number of hours left and 24 - h represent the number of hours passed.

2. I'm thinking of two consecutive numbers. When I multiply the greater number by 3, I get 9 less than 5 times the other number. What are the two numbers?

Answer: 6 and 7. You can definitely write and solve an equation to solve this problem. Trial and error works nicely here, too. Just test small consecutive numbers until you find two that work.

3. I built a square fence using 48 posts. I placed the posts 5 meters apart. What is the area of the field bounded by the fence?

Answer: 3600 square meters. Drawing a picture is a great way to solve this problem. There are twelve 5-meter spaces between posts on each side. Thus, each side length is 60 meters. Base X height or 60 X 60 = 3600.

 

4. 4. Replace each letter with a different digit to make a true equation. Identical letters should be replaced with the same digit.

Answer: P= 2, A= 1, R= 9, T= 7, S= 8. Blind trial and error on a problem like this will drive you absolutely crazy. Try to look for clues that show you the relationships between letters and their values. For example, we know by looking at the problem that S ´ 4 = P. Since P is a single-digit number, S must either be 1 or 2. Continue to work the problem piece by piece looking for similar clues.

5. What is the difference between two dozen half-dozens and a dozen dozens?

Answer: Nothing. They are the same! Two dozen half dozens can be expressed as 24 X 6 which equals 144. A dozen dozens can be expressed as 12 X 12 which also equals 144.

6. What is the difference between half a dozen half-dozens and half of a half-dozen?

Answer: 33. Half a dozen half-dozens can be expressed as 6 X 6 which equals 36. Half of a half-dozen can be expressed as ½ X 6 which equals 3. The difference between 36 and 3 is 33.