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If the average of 4 numbers must be 100, that means that all the numbers have to add up to 400. This is because if you divide 400 by 4, which is the number of integers, the outcome would be 100.
After, I found that the smallest integer would be 1, and the biggest integer would be 394. This is because the next 2 smallest numbers would add up to 5, so that means that the biggest number must be 394. The next 2 smallest numbers would be 2 and 3. This is so that all the 4 numbers would add up to 400, and have an average of 100.
So if you would subtract 394 and 1, you would get the biggest difference. The other two integers are 2 and 3. If you add the numbers, you would get 5. Then if you divide 5 by 2, you would get the average of the two.
Therefore, the average of the other two integers is 2.5
Grade 7 POTW: How I did it was to figure out the largest number possible. Of course, that cannot be a number larger than 4*100=400, and also the number cannot be larger than 394. The reason for this is because all numbers are different, so I have to choose the smallest possible consecutive group, which is 1,2, and 3. This adds up to 6. So, 400-6=394. Therefore, 394 is the largest possible number.
The two middle numbers are 2 and 3. These average to 2.5, since (2+3)/2=2.5. That is the answer to the first part.
I am not very sure about the second part, but I think that the answer is 10%. This is because the picture has "Average" written on it, meaning we would have to find the average. There are also 10 percent signs, meaning that there are 10 numbers we need to average. The only part we are missing is the total. I can assume that the total is probably 100 because they are percent signs, and the total would be 100%. So, averaging it out, I would get 10% since 100/10=10.
The average of the other 2 numbers is 2.5. This is because the largest difference would be with the smallest number possible being 1. Then the largest number to make 400 because the total would be 100*4. 400-1=399. But since there are 2 other numbers those would be 2 and 3 so all numbers would be 1,2,3 and 394(399-(3+2)=394). Then the other 2 numbers would be qualified as 2 and 3. 2+3=5, 5/2=2.5.
Grade 7: There are 4 integers meaning the total sum of the numbers is 400 with the average of 100. 1+2+3+394=400 The biggest difference is 392. The picture puzzle represents an average of 10% a there are 10 percent signs.
To solve this question I need to find the largest possible number and the smallest possible number. For the average of 4 numbers to be 100, they must sum 400. The smallest possible number would be 1, the largest would be 394 and the other two numbers would be 2 and 3. This is because the smallest 3 numbers would 1, 2 and 3 add up to 6 so I subtracted 6 from 400 to get my final (and biggest number) and I got 394.
394 + 1 + 2 + 3 = 400
The question asks me to find the average of the 2 middle integers (2 and 3 (2 + 3) / 2 = 2.5
The average of the two other numbers is 2.5.
The answer to part 2 of the question is 10% above average. Mr. Milette told me the answer but the reason it is the answer is because there are 10 % signs above the word Average. So it became 10 % above average.
Grade 7 POTW: I know that the sum must me 400, since the average of the four numbers is 100, 100*4= 400. Then, using some logic... I knew that 1 must be the smallest number 2 is the 2nd smallest number 3 is the 3rd smallest number 394 is the biggest number, now that we know all the numbers, we can figure out the average of the 2 numbers.
For this question, I figured that I had to find 4 numbers that added up to 400, and that the numbers had to be whole numbers above zero. In order to make their the largest difference between the largest and smallest integers, I started with the smallest 3 numbers that fulfilled the requirements, 1, 2, and 3. Since those added up to 6, I used subtraction to find that the final number was 394.
Since the question asked to find the average of the two middle integers, which were 2 and 3, I divided the sum (2+3) by 2, which gave me 2.5. Therefore, the average of the two middle integers in the puzzle would be 2.5.
For the second part of the question, I thought that it meant be 10% better than average. This is because there are 10 percent signs, which are above the word average.
Here is how I solved the Grade 8 POTW: First I found the number the four numbers would add up to: 2017 x 4 = 8068 Then I took the ones digit and found ones digits from the other numbers that added up to a number with the ones digit of 8: 7 + 8 + 9 + 4 = 28 I then used these numbers: 1867 + 2139 + 2028 + 2034 = 8068 it's a match! So 1994 and 2126 are the remaining numbers: 1994 + 2126 = 4120 4120 / 2 = 2060 The average of the remaining numbers is 2060.
For the extra part of the Grade 8 POTW When I first look I see, B > BE MORE
and then there is a bunch of sigma notation.
which I guess means ( from what I know about sigma notation) that x^1 + x^2 + x^3... all the way to x^n and all of that equals x(1) ?!?!?! so... x is just one? eh...?
Be more than one????
What about 1/n?
uhhh....
* 5 min later while searching around about sigma notation, finds " sigma notation average" in recommended bar Me: hmm...? * looks at images* OHHHHHH!!!!
That WHOLE second part just means average... i think :/
Here is how I went about solving the Grade 7 POTW: Since it says the average of four numbers is 100, 100 x 4 = 400. I used the largest possible number (399), and the smallest (1) to give me 400. But there still needed to be two more numbers. This meant that I would have to use the next two smallest numbers (2,3). After doing this, I added them up to make sure they equaled 400, and they did! So since we have to calculate the average of the two middle numbers, we do 2 + 3 = 5, and then divide 5 by 2. This gives us 2.5. Therefore, the average of the two "other" numbers is 2.5.
Word problem: I thought that the answer was 10% average because there are 10 percent signs and then an average sign after it. But it turns out that the answer was actually 10% above average.
How I solved this problem was that I first added all the numbers together to get 12188. Next since 4 of the numbers has the mean of 2017 then I multiply 2017 by 4 to get 8068. Next I subtract 8068 from 12188 to get 4120. Finally I divide 4120 to get 2060. Thus the average of the two numbers is 2060.
I solved this problem by finding the total of all of the numbers, and then subdracted it by 2017 x 4 as 4 numbers have a mean of 2017. Using this, I can get the mean of the two numbers by dividing this value by 2.
All six numbers: 12,188 2017 x 4 (4 numbers have mean of 2017) = 8068 = 12188 - 8068 = 4120 4120/2 = 2060
Grade 7 POTW:
ReplyDeleteIf the average of 4 numbers must be 100, that means that all the numbers have to add up to 400. This is because if you divide 400 by 4, which is the number of integers, the outcome would be 100.
After, I found that the smallest integer would be 1, and the biggest integer would be 394. This is because the next 2 smallest numbers would add up to 5, so that means that the biggest number must be 394. The next 2 smallest numbers would be 2 and 3. This is so that all the 4 numbers would add up to 400, and have an average of 100.
So if you would subtract 394 and 1, you would get the biggest difference. The other two integers are 2 and 3. If you add the numbers, you would get 5. Then if you divide 5 by 2, you would get the average of the two.
Therefore, the average of the other two integers is 2.5
Grade 7 POTW:
ReplyDeleteHow I did it was to figure out the largest number possible. Of course, that cannot be a number larger than 4*100=400, and also the number cannot be larger than 394. The reason for this is because all numbers are different, so I have to choose the smallest possible consecutive group, which is 1,2, and 3. This adds up to 6. So, 400-6=394. Therefore, 394 is the largest possible number.
The two middle numbers are 2 and 3. These average to 2.5, since (2+3)/2=2.5.
That is the answer to the first part.
I am not very sure about the second part, but I think that the answer is 10%. This is because the picture has "Average" written on it, meaning we would have to find the average. There are also 10 percent signs, meaning that there are 10 numbers we need to average. The only part we are missing is the total. I can assume that the total is probably 100 because they are percent signs, and the total would be 100%. So, averaging it out, I would get 10% since 100/10=10.
--Alan
The average of the other 2 numbers is 2.5. This is because the largest difference would be with the smallest number possible being 1. Then the largest number to make 400 because the total would be 100*4. 400-1=399. But since there are 2 other numbers those would be 2 and 3 so all numbers would be 1,2,3 and 394(399-(3+2)=394). Then the other 2 numbers would be qualified as 2 and 3. 2+3=5, 5/2=2.5.
ReplyDeleteGrade 7: There are 4 integers meaning the total sum of the numbers is 400 with the average of 100. 1+2+3+394=400 The biggest difference is 392. The picture puzzle represents an average of 10% a there are 10 percent signs.
ReplyDeleteGrade 8 POTW Part 2:
ReplyDeleteAfter doing some researching, I found out that the graphic means that B is larger than the average of X1 added up to Xn.
So, if Xn = 3, then it would be B>(X1+X2+X3)/3.
(Dunno if this is right, but I'll give this a shot anyways)
-Alan
Grade 7 Potw:
ReplyDeleteTo solve this question I need to find the largest possible number and the smallest possible number.
For the average of 4 numbers to be 100, they must sum 400.
The smallest possible number would be 1, the largest would be 394 and the other two numbers would be 2 and 3. This is because the smallest 3 numbers would 1, 2 and 3 add up to 6 so I subtracted 6 from 400 to get my final (and biggest number) and I got 394.
394 + 1 + 2 + 3 = 400
The question asks me to find the average of the 2 middle integers (2 and 3
(2 + 3) / 2 = 2.5
The average of the two other numbers is 2.5.
The answer to part 2 of the question is 10% above average. Mr. Milette told me the answer but the reason it is the answer is because there are 10 % signs above the word Average. So it became 10 % above average.
Grade 7 POTW:
ReplyDeleteI know that the sum must me 400, since the average of the four numbers is 100, 100*4= 400. Then, using some logic...
I knew that 1 must be the smallest number
2 is the 2nd smallest number
3 is the 3rd smallest number
394 is the biggest number, now that we know all the numbers, we can figure out the average of the 2 numbers.
(2+3)/2=2.5
The average of the two middle numbers is 2.5.
For this question, I figured that I had to find 4 numbers that added up to 400, and that the numbers had to be whole numbers above zero. In order to make their the largest difference between the largest and smallest integers, I started with the smallest 3 numbers that fulfilled the requirements, 1, 2, and 3. Since those added up to 6, I used subtraction to find that the final number was 394.
ReplyDeleteSince the question asked to find the average of the two middle integers, which were 2 and 3, I divided the sum (2+3) by 2, which gave me 2.5. Therefore, the average of the two middle integers in the puzzle would be 2.5.
For the second part of the question, I thought that it meant be 10% better than average. This is because there are 10 percent signs, which are above the word average.
Here is how I solved the Grade 8 POTW:
ReplyDeleteFirst I found the number the four numbers would add up to:
2017 x 4 = 8068
Then I took the ones digit and found ones digits from the other numbers that added up to a number with the ones digit of 8:
7 + 8 + 9 + 4 = 28
I then used these numbers:
1867 + 2139 + 2028 + 2034 = 8068
it's a match! So 1994 and 2126 are the remaining numbers:
1994 + 2126 = 4120
4120 / 2 = 2060
The average of the remaining numbers is 2060.
For the extra part of the Grade 8 POTW
ReplyDeleteWhen I first look I see,
B >
BE MORE
and then there is a bunch of sigma notation.
which I guess means ( from what I know about sigma notation) that x^1 + x^2 + x^3... all the way to x^n and all of that equals x(1) ?!?!?!
so... x is just one?
eh...?
Be more than one????
What about 1/n?
uhhh....
* 5 min later while searching around about sigma notation, finds " sigma notation average" in recommended bar
Me: hmm...?
* looks at images*
OHHHHHH!!!!
That WHOLE second part just means average... i think :/
SO...
BE MORE THAN AVERAGE!
Here is how I went about solving the Grade 7 POTW:
ReplyDeleteSince it says the average of four numbers is 100, 100 x 4 = 400. I used the largest possible number (399), and the smallest (1) to give me 400. But there still needed to be two more numbers. This meant that I would have to use the next two smallest numbers (2,3). After doing this, I added them up to make sure they equaled 400, and they did! So since we have to calculate the average of the two middle numbers, we do 2 + 3 = 5, and then divide 5 by 2. This gives us 2.5. Therefore, the average of the two "other" numbers is 2.5.
Word problem:
I thought that the answer was 10% average because there are 10 percent signs and then an average sign after it. But it turns out that the answer was actually 10% above average.
How I solved this problem was that I first added all the numbers together to get 12188. Next since 4 of the numbers has the mean of 2017 then I multiply 2017 by 4 to get 8068. Next I subtract 8068 from 12188 to get 4120. Finally I divide 4120 to get 2060. Thus the average of the two numbers is 2060.
ReplyDeleteI solved this problem by finding the total of all of the numbers, and then subdracted it by 2017 x 4 as 4 numbers have a mean of 2017. Using this, I can get the mean of the two numbers by dividing this value by 2.
ReplyDeleteAll six numbers: 12,188
2017 x 4 (4 numbers have mean of 2017) = 8068
= 12188 - 8068 = 4120
4120/2 = 2060
The mean of the two numbers is 2060.
I Am starting to do most potw's on paper so i normally don't post the comment
ReplyDelete