Hurricane Katrina (and a little bit of the labour day long weekend affect) were the reason the gas prices skyrocketed. As for the Grade 7s, a manager will almost surely make more money than an employee, usually regardless of years of service. This is how most business hierarchies work. So in that case, Jessica would most likely have the highest salary (way to go Jessica, you've earned every penny).
For specific answers, please review the postings & replies from POTW #1. POTW #2 is below:
Grade 7 POTW #2 Question:
Grade 8 POTW #2 Question:
Grade 7 POTW
ReplyDeleteKhan Kickit kicked 5 times. His longest kick was 44 yards and the mean kick was 35 yards. All kicks had different lengths. This is the only data needed to find the minimum length. First, let's find out what the mean is. The mean is all the integers in a data set added together and then dividing that sum by the amount of numbers. If we work backwards from there, we'll find our answer. 35, the mean x 5, the amount of numbers is 175. Getting rid of 44 (because that value is already confirmed) leads to 131. To get the lowest kick distance, you need the highest possible lengths. The next highest after 44 is 43, 42, and 41. 43 + 42 + 41 = 126. 131 - 126 is 5. This means 5 is the minimum distance in yards that he could've kicked.
Khan Kickit kicked a minimum of 5 yards for one kick.
Grade 7 POTW:
ReplyDeleteI'll first do this one since I haven't looked at the grade 8 one yet :)))
He kicked the ball 5 times with a mean of 35 yards per kick, which means the total distance of his kicks is 35*5 = 175 yards. Since his longest distance kicked was 44 yards, then all of the lengths must be under or equal to 44. To find the minimum distance, we would have to assume that all of his kicks except for 1 is 44. This gives me 44*4 = 176, which is 1 over. What I can do is change one of the 44's to 43 so it adds up to 175.
I'm assuming that it allows for your distance to be zero(Which probably means that he missed the ball) so the minimum distance would be 0. (Unless he can kick the ball a meter backwards?!) Even if it can't be zero, I guess I should find the smallest value, which is like smaller than a millimeter so I'm not going to go that far and find that, which is why I assumed that the minimum distance is 0.
-Alan
Grade 8 POTW:
ReplyDeleteFirst of all, to find out the largest possible value I can get I first need to figure out the number of tokens in the bag. To do this, I will use the information given in the question.
I decided to do it using algebra, but if you do these types of problems long enough, you should be able to figure out immediately. Here is how to do it in algebra:
Let x be the number of tokens in the bag.
56x = 55x + 68.
56x is the original value, which is the total value of these 56 tokens, while it equals the total value of 55 of these tokens, and the 56th one being 68.
So, after simplifying I would be able to get x = 68.
Thus, there are 68 terms, which means that there are 68 tokens in the bag.
Since the question states that more than one token can have the same number, I can literally pretend that 67 of the tokens have the value of 1 on it(since the number has to be a positive). This gives me 67 in total. To figure out the maximum number I would have to first find out the total of the tokens, which is 56*68 = 3808, then subtract it by 67. So, 3808-67 = 3741.
THEREFORE, the largest possible integer that could appear on one of the tokens is 3741. What a large number for a mean of 56!
Okay. I didn't quite understand that. What is your final data set for the mean being 56?
DeleteGrade 7 POTW cont. :
ReplyDeleteMy mistake! I did not realize that they had to be different lengths. So, instead of all being 44s, it is actually 44,43,42,41 and the minimum which is 170. Since the total distance he kicked was 175 yards, as I figured out from before, his minimum kick was 5 yards.
-Alan
Grade 8 POTW
ReplyDeleteThe facts needed are all the tokens are positive integers, tokens can have the same number as other tokens, the mean is originally 56, and once 68 is removed, then the mean becomes 55. We need to know the largest possible integer that can appear.
Now, if the mean is originally 56 and let's just pretend the number of numbers is 3 for this example, then 56 x 3 - 68 should = 55 x 2. So 56y - 68 = 55(y-1).
After some trial and error, I came up with this. y=13. 56 x 13 = 728. 728 - 68 = 660. 55 x (13-1) = 660. No other value works.
Now, like said before, multiple tokens can have the same value. 660 is the number we work with for values. There must be 12 integers that when add up, the sum is 660. You also need to include the largest possible integer. All 11 values can easily be 0 leaving the largest value to be 660.
In conclusion, the largest possible integer should be 660.
The data set in this case will be 660, 68, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.
Sorry. 0 isn't considered as a positive integer so it's supposed to be 1. 660 - 11 is 649. The data set will be 649, 68, and then the 11 1s. The largest integer will then be 649.
DeleteSorry again. Messed up. 68 doesn't have to be an option. Plus I forgot about doing 56x=55x+68 and then 56x - 55x = x or 68.
Deletelet x represent the sum of all the tokens
ReplyDeletelet y represent the amount of tokens
to find an average you need the sum of all the numbers and the amount of numbers then to divied the sum by the amount. in this situation it will be
x
--=56 mulyiplyboth sides by y
y
x=56y
without 68 it will be
x-68
-----=55 multiply bothsides by y-1
y-1
x-68=55(y-1) open brakets
x-68=55y-55 insert y
56y-68=55y-55 put all y's to oneside
-68+55=-55y+56y solve
13=y there are 13 numbers
find x
x=56y
x=13 times 56
x=728
tofind the highest posible number we know that 1 of 13 numbers =68 so
728-68= 660
if the lowest number can be 1 then the highest number is 660-11=649
therefor 649+1+1+1+1+1+1+1+1+1+1+1+68=728
728/13=56
First I will find how much all his kicks should add up to by multiplying the mean/ average by the number of kicks there were:
ReplyDelete35 yards x 5 = 175 yards
I know that his furthest kick is 44 yards, so I should subtract it from the total.
175 yrds - 44 yrds = 131 yrds
Now the rest of the kicks should add up to 131 yards, but none of them can be greater than 44 yards. I know that the smallest positive integer is 1, so I can try using that.
131 - 1 = 130
Now the last 3 kicks should add up to 130. The last three kicks could be any numbers, just bigger than 1 and smaller than 44. The three kicks can be: 43, 43, and 44. Since 44 isn’t larger than his longest kick, it could be a possibility.
His kicks are 1, 43, 43, 44 and 44.
Double check: 1 + 43 + 43 + 44 + 44 = 175
175 / 5 = 35
The mean is 35
The median is 43
The mode is 43 and 44
The range is 43
It actually can't be 44 again as the question states that each of kicks had different values.
Deletei dont think you need the Central Tendencies and the range. Do we?
DeleteJust read the question. It didn't state we had to so no.
DeleteGrade 8 POTW
ReplyDeleteTo solve this question, I first have to find how many tokens are in the bag. To do this I will make an algebraic equation.
let x equal the amount of tokens.
56x = 55x + 68
-55x -55x
x = 68
There are 68 tokens in the bag. to find the sum of all the tokens, I have to solve the problem backwards. I know that I have to divide the sum of all the numbers to get the mean. That means I have to multiply the mean by the amount of numbers to find the sum of all the numbers.
56 * 68 = 3808.
To find the highest possible integer, all the other numbers have to be 1(the lowest possible integer). That means that 67 of the tokens are equal to 1.
67 * 1 = 67.
3808 - 67 = 3741.
The highest possible integer is 3741.
Grade 7 POTW
ReplyDeleteTo solve this problem, the first thing I need to do is find the total of all the kicks. I have to solve the mean backwards to do this. I have the mean, 35 and I have to multiply that by the total amount of kicks he took (5).
35 * 5 = 175.
I know one kick is 44 yards so I can subtract that from the total.
175 - 44 = 131 yards.
The remaining 4 kicks should add up to 131 yards. To get the minimum possible amount of yards he kicked, the other numbers have to be the highest possible. Those numbers are 43, 42 and 41.
43 + 42 + 41 = 126
131 - 126 = 5
The minimum possible length he kicked is 5 yards
Grade 8 POTW
ReplyDeleteFirst, I decided to make an equation to find out the number of tokens in the bag, with x being the unknown.
55x+68=56x
68=56x-55x
68=x
Therefore, there are 68 tokens in the bag.
Next, I have to find out the amount that all the tokens add up to, by multiplying the mean of the tokens by the amount of tokens, which equals 3808. Because each token has a positive integer on it, each token must have a number equal to or higher than 1, so if each token was 1, except for one of them, the other token would equal 3808-67, or 3741. Therefore, the highest number possible on any token is 3741.
But isn't 1 token already 68 so wouldn't the end part be 3808-(66+68)?
DeleteNo, you would have to subtract by 67 and not 134 because in order to find the largest possible integer, one would have to assume that all of the other tokens have a value of 1. That way the lowest numbers could match with the highest number and still have a mean of 56.
DeleteHere is how I went about solving the Grade 8 POTW:
ReplyDeleteI decided to use algebra since it is good practice and the simplest way to break down this question.
Let x = the total number of tokens in the bag
56x = 55x + 68
Now subtract 55x from each side. This leaves you with...
1x = 68
Therefore, there have to be 68 tokens in the bag and "x" is equal to 68.
Now I would have to multiply the total amount of tokens in the bag, by the average value of all tokens in the bag.
68 * 56 = 3808
Now in order to find the largest possible number, we would have to calculate that all of the other 67 tokens have a value of 1.
3808 - 67 = 3741
Therefore, the largest possible integer that could appear on one of the tokens is 3741.
Grade 8 POTW
ReplyDeleteSuppose x is the total amount of tokens
Remaining integer: 56x-68
Remaining integer: 55(x-1)
56x-68=55(x-1)
56x-68=55x-55
Isolate x
56x-55x=-55+68
x=13
Before 68 was taken out, there were 13 numbers. Since 68 was taken out, there are now 12
Because the numbers have to be an integer and could recur, we could assume all the other 11 numbers could could be 1.
To find the highest number do the operation of finding thr average backwards
55×12-11=649
The largest number is 649
Grade 8 POTW:
ReplyDeleteFirst off, I have to find out how many tokens are in the bag. I would do this by using an algebraic equation which is
Let x represent the amount of tokens in the bag
56x = 55x + 68
68 = 56x - 55x
68 = 1x
x = 68
Now that we know there are 68 tokens in the bag, we can get to work. Since the average of the remaining tokens is 56, we will multiply the amount of tokens in the bag by the average.
56 x 68 = 3808
Now since we are trying to find the largest integer, we must assume that all of the remaining 67 tokens must have a value of 1.
67 x 1 = 67
Since we know that all of the remaining token's values added together is 67, we can subtract that from 3808.
3808 - 67 = 3741
The largest possible integer that can be on the token is 3741.
Grade 7 POTW #2:
ReplyDeleteSince we know that Khan kicked the ball five times and got an average of 35 yards, we can easily figure out the total distance kicked by multiplying 35 by 5... 35 x 5 = 175 (that's all five of the kick lengths added up).
Since we already know the length of one of the kicks (44), I can subtract that from the total. 175 - 44 = 131. This means that the 4 kicks left must add up to 131 yards.
Because it says that it has to be a positive integer length, I decided to start with the minimum, which is 1. If one of the kicks was 1 yard, that means that 3 kicks would have to add up to 130. However, I have to remember that each kick was a different length, and that I cannot go over 44.
The way I checked if this was possible was to take the 3 numbers under 44 and add them up to see if it goes over 130. 43 + 42 + 41 = 126. This means that it is not possible for one of the kicks to be 1.
I didn't bother trying 2, 3, or 4, because all of those numbers are too small and won't make the total reach 131. So the smallest number that could work would be 5.
(To check: 44 + 43 + 42 + 41 + 5 = 175. Yay!)
The minimum possible length of Khan's shortest kick is 5.
GRADE 7 POTW
ReplyDeleteImportant Info:
- 5 kicks
- Average is 35
- Longest kick= 44 yards
- All values are different.
Work:
Since I need to know the sum of the numbers to find out the lowest possible length, I will need to reverse the rule of finding the average. Instead of adding up the numbers then dividing, I need to multiple then subtract. Since the average is 35 and the number of kicks is 5, I multiple 35 by 5, which gives me 175. Now, I know that the sum of the lengths of the kicks is 175. Since the farthest is 44 yards, I can subtract that from the sum. 175-44=131. The remaining four numbers have to add up to 131. Since I need to find the lowest possible distance, I need to subtract the largest possible numbers. Due to the fact that 44 yards is the longest distance, I know that every number has to be below 44 yards. I can try to subtract 43, 42 and 41. 131-43=88, 88-42=46, 46-41= 5.
DOUBLE CHECK:
5+41+42+43+44= 175.
The lowest possible length has to be 5.
For the grade 8 potw I first solved for the amount of tokens in the bag. 56X=55X+68 or X=68 so there are 68 tokens in the bag. Then the total value of all the tokens is 55*68 or 3740. Then if we want to find the largest token then we subtract 54 from 3740 to get 3686 so that is the largest possible integer (Looking through the comment section a lot of people got 3741 as the integer but that was including the one 68 token that was taken out without using one of the tokens as 68 or just having that token taken out).
ReplyDeleteWhy 54? You said there are 68 tokens. Also, can you tell me your final data set. You can just say for example 48 1s.
DeleteI figured out the base with a simple way of figuring out the tokens in the bag because I would have no basis without this. After this, I found out with 68 being removed, and the value decreasing by 1, that there must be 68 tokens in the bag. After this, multiplying the old average by the number of tokens would leave me with 3808. However, it is impossible for 0 to be considered positive, so you must make them 1s, subtracting the number of tokens after 68. This means that the largest integer that could appear on a singular token is 3741.
ReplyDeleteGRADE 7 POTW:
ReplyDeleteIf 35 is the mean, it means that the 5 kicks that khan kicked have to all equal 175 because 175/5 is 35.
Since we already know one of the hits (44), We have to just take 175 and subtract 44 from it.
175 - 44
= 131
Then, we take the highest value that's lower than 44 (43) and subtract that from 131
131 - 43
= 88
After that, We'll take the number lower then 43 and subtract that from 88
88 - 42
= 46
Finally, we subtract the highest value lower then 42 from 46
46 - 42
= 5
Now, we got all of our 5 numbers that was subtracted from 175; 44,43,42,41,5. 5 Is our lowest number, so that means it's Khan's lowest kick
The shortest distance Khan kicked is 5 yards.
Grade 8 POTW
ReplyDeleteNow like a lot of other students, algebra would probably be the best way to solve this problem, since you can simplify the question by breaking it down and solving one component at a time.
The problem is asking us to find the largest possible integer out of all the tokens in that bag, but we have to first find out how many there are in order to find out the largest possible integer.
So using my algebraic knowledge, lets find the total amount of tokens
Let x= The number of tokens
56x= 55x+68
56x-55x= 68
x= 68
Now that we have the total number of tokens, we can then find the largest number using the information given. We know that the total number of tokens in the bag is 68, and the average of all of those tokens is 56. So..
68*56= 3808
But that doesn't give us the largest number. In order to get that, we must use our imagination.
Let's say that all 67 of the tokens were equal to 1 (the lowest possible integer). If I were to add all of those tokens up I would get 67. Now to find the largest number, all we have to do is subtract this from 3808. So..
3808-67= 3741
We now know that the largest possible integer out of all the tokens in the bag must be 3741!
Oh. Now I understand a lot more. My mistake. I thought 68 must be a value. Thanks Amber.
DeleteGradee 8 POTW Numero 2:
ReplyDeleteTo find the highest possible integer, II must first find the total number of tokens in the bag. To do so, I take x as the number of tokens there are, and write out, 56x. This is equal to 55x+68, as the question has stated. This means 68+55x=56x, 68=56x-55x, 68=x. Because of this, there are 68 tokens in the bag. After finding this, I would have to assume that the other 67 tokens are the lowest possible value, and as the question stated, there can be more than 1 of each number, which means all 67 numbers could be one. To find the total of all the numbers, you do 56x68, which is 3808. Now to find the highest possible number, you take 3808 and subtract 67 from it, leaving you with 3714 as the highest possible value.
grade eight potw
ReplyDeleteso i did look at previous answers because i was completely lost.
WHAT WE ARE LOOKING FOR:
-highest possible integer in the bag of tokens
how to do it:
so we are given the original average, 56
after removing the toekn with "68" the average becomes 55
Therefore we will need to find the total amount of tokens.
x=tokens
68 + 55x = 56x
68 = 1x
68 = x
There are 68 tokens.
And now we find the sum of the tokens.
68 x 56 = 3808
(assuming the average is using the mean)
and now we have to find the highest possible value of 1 token.
Assuming that, the best way to guarantee it is to have the other tokens be the lowest possible integer. Giving a large range between the 1 highest integer.
1 is the lowest positive integer. Therefore is 67/68 tokens were 1, leaving the final token to be the "highest possible integer", that token would have the number 3741.
Grade 8 POTW
ReplyDeletex = number of tokens in bag
56x=55x+68
simplified to 1x=68
68 tokens in bag
Amount of tokens in bag (68) multiplied by the average value of tokens (56) is 3808
The other 67 tokens can be assumed to be 1 to find the largest possible value
3808-67=3741
The largest possible integer for the average to be 56 is 3741
a=sum of all token numbers
ReplyDeleteb=number of tokens
56x=55x+68 >>>>>> x=68
68x56=3808
3808-68=3741
3741
I found that the lowest amount of yards would be 5. I know this because to find the average, I would just have to add 5 different numbers and divide them by five. I found my answer by finding 4 different numbers ( 44,43,42,41) which equaled to 170 but I needed to get the number 175 in order to get an average of 35 so I added 5 which would be his shortest kick.
ReplyDeleteCONFERMATION: 44+43=87+42=129=41=170+5= 175
Yay!
Grade 7 POTW
ReplyDeleteWe start with the information we know:
- Overtime he kicked, the ball went a different distance
- his longest kick was 44 yards
- x/5=35
Work
based on the last piece of info, we can work backwards:
35x5=175 so, 44+(x)+(x)+(x)+(x)= 175
we know that both there can't be another 44 yard kick, and all the other kicks are less
the rest of the kicks have to add up to 175
if we do 175-44 we get 131 which is what the other numbers have to add up to.
lets try: 42+43+41+5=131! i know that five is the lowest possible kick because if we were to make any of the bigger numbers bigger they would repeat.
lets check it.
44+43+42+41+5=175
175/5=35
Judging by khans kick lengths, i would say that Khan is a horrible football player and has no chance to get into the NFL.
For this question I solved for the total of tokens in the bag. 56X=55X+68 or X=68, therefore I think that there are 68 tokens in te bag. Because of this the tokens are worth 3740. Thhe biggest token could be no bigger than 3741.
ReplyDeleteForgot to send a message but i did this on paper. The biggest token could be 3741
ReplyDeleteGrade 8 POTW:
ReplyDeleteI don't think my full answer went through for this one. The answer would 3741 as the biggest token.
*Late*
ReplyDeleteLike Michelle, I was having trouble on solving this, so I read a couple answers before finally somewhat understanding the problem and how to do it.
I did my work in my notebook.
Final:
The largest numbered token can be 3741.