Two winners for October Math Mania contest

Two kids who entered the October Math Mania competition got all seven answers correct. Many of you figured out the answer to the tricky first question.

The October winners with all answers correct were two 12-year-olds, Chrissy Macek and Beth Johnston. Beth also was a winner in the September Math Mania.

Since there were less than three winning entries, both kids will be given $10 Borders gift certificates.

The tricky first question said 30 per cent of people in a town had unlisted telephone numbers. Then, it asked, if 200 people in the book were called randomly, now many would you expect to have unlisted numbers.

Some of you figured the answer as 60 (30 per cent of 200). But, the answer was Zero. That's because people with unlisted numbers couldn't be called from phone book numbers.

Here are the answers to the October questions:

October Math Mania

1. Thirty percent of the people in a certain town have unlisted phone numbers. You select 200 people at random from the phone book. What is the expected number of people who will have unlisted phone numbers?

Answer: 0. If people have unlisted phone numbers, then they won't be selected from the phone book!

 

2. Using the following numbers, how many different ways are there to add 3 numbers to make a sum of 10? A number can be used more than once, but a group cannot be repeated in a different order (e.g., 3+2+1 is the same as 2+3+1).

Answer: 8. I suggest making an organized list, starting with the largest number. For example, I found all of the combinations using 8, then 7, then 6, and so on…

8+1+1	8+2+0	7+2+1	6+2+2
6+4+0	5+4+1	5+5+1	4+4+2

 

 

3. A frog ate 104 bugs in 4 days. Each day he ate 10 more than on the previous day. How many did he eat each day?

Answer: 11, 21, 31, and 41. An equation will make this problem a breeze.

Let x represent the first day. Then, day two will be 10 more or x + 10. Day three will be 10 more than day two or x + 20. Day four will be 10 more than day three or x + 30.

Since the sum of the four days is 104, set up and solve the equation as follows:

x + x +10 + x + 20 + x + 30 = 104

4x + 60 = 104

4x = 44

x = 11

Eleven is the number of bugs on the first day. To find the second day, add 10 and so on…

If you didn't use an equation to solve this problem, try one next time! Once you get the hang of it, it's easier than trial and error.

 

4. Find the reciprocal (in lowest terms).

Answer:

 

5. What number is as much greater than -12 as it is less than 18?

Answer: 3. Since the average of two numbers is located directly between those numbers, find the average of -12 and 18. You can also illustrate the problem with a number line.

 

6. Move one number to another group so the sum of the digits in each group will be equal.

Answer: Move the 9 to the first group so that all of the groups total 15.

 

7. Use five 4's to make an equation that equals 261. Any mathematical operations and symbols may be used. Be sure to follow the correct order of operations!

Answer: 4 + 4 + 4 ÷ 4. Other solutions may exist as well. That is the beauty of math!