POTW #11 Answer:
Where are the full sentences!!!!!!!!!!!!!!!
Solution:
1 - ½ = ½
½/2 = ¼
¼/2 = ⅛
⅛ = 0.125 = 12.5%
¼ + 8 km = 1
8 km = ¾
8/3 = 2.66…
2.66… + 8 = 10.66… km
10.66… = 10.66.../100 = 1066.6...% = 10 2/3
⅛ + ⅛ + ½ + 1 = ¼ + 2/4 + 1 = 1 ¾ of apples
1 ¾ = 1.75 = 175%
⅛:1 ¾ (already simplified)
Grade 7/8 POTW
ReplyDeleteFirst, I'll list the data:
x, x, x, 22, x, 45
Facts:
The mean of the 2 values before a value is the value.
I can just work from there.
Starting from the sixth number (because a value in the range of 2 is the 4th value). Working backwards from 45, 45 x 2 (to find the sum of the fifth and sixth) = 90. 90 – 22 = 68. The fifth value is 68.
x, x, x, 22, 68, 45
Using the same strategy for the fifth value. 68 x 2 = 136. 136 – 22 = 114. The third value is 114.
x, x, 114, 22, 68, 45
22 x 2 = 44. 44 – 114 = -70. The second value is -70.
x, -70, 114, 22, 68, 45
114 x 2 = 228. 228 - - 70 = 298. 298 is the first value. These are all the final values for each number, the 6 numbers.
298, -70, 114, 22, 68, 45
POTW:
ReplyDelete#1:
#2:
#3:
#4:22
#5:
#6:45
To find number 5, we multiply 45 by two and subtract 22 from it. 90-22=68. So the number must be 68
#1:
#2:
#3:
#4:22
#5:68
#6:45
Next to find number 3 out. We have to multiply 68 by 2 and subtract 22 from it. So it's 114.
#1:
#2:
#3:114
#4:22
#5:68
#6:45
And we can continue this, but #2 must be a negative integer because 114 is already a lot higher than 22.
So we have:
#1:298
#2:-70
#3:114
#4:22
#5:68
#6:45
We can check this. So (298+ -70)/2 should be 114.
(298+-70)/2
=228/2
=114. And yay it works.
So the sequence is:
#1:298
#2:-70
#3:114
#4:22
#5:68
#6:45
Since we have the numbers 4 and 6 values, we need to work our way back, starting from 5. the average of 22 and x is 45. So therefore number 5 is 68 through the mean formula. Number 5 is the average of number 3 and 22, so number three is 114 through the mean formula. 22 is the average of 114 and number 2, so therefore number 2 is -70 through the mean formula. 114 is the average of number 1 and -70, so therefore the number one is 298 from the mean formula.
ReplyDeleteSo with the information I have right now, I can only determine the 5th number. Since that number would be (x+22)/2=45, I would first multiply 45 by 2 which gives me 90.
ReplyDeleteThen, I subtracted 22 from 90 to get x, which was 68.
Then, I moved on to the 3rd number. I now know that the 5th number is 68 and the 4th number is 22, so it would be (x+22)/2=68. Like the last one, I did:
68x2=136
136-22=114
So, the 3rd number is 114.
Now, I have to get the 2nd number. I repeated the process from the last 2 numbers to get this.
22x2=44
44-114=-70
So, the 2nd number is -70.
Then finally, I calculated the 1st number.
114x2=228
228--70=228+70
=298
So, when I put all of these together, the sequence is:
298, -70, 114, 22, 68, 45
Grade 7/8 POTW:
ReplyDeleteSequence:__,__,__,22__,45
Info:
- Each number is the average of the the last 2 numbers.
Find all 6 numbers.
The trick for this question
To answer this, I have to work backwards.
5th value: To find the 5th value, I have to mutiply 45 by 2 to find the sum and subtract 22 to find the 5th value (because 45 is the sum of 22 and x divided by 2). (45 x 2)-22=68. The fifth value is 68.
Sequence: __,__,__,22,68,45
I can use this same strategy to find the 3rd value (68 x 2)-22=114. And for the rest of the values:
Sequence: __,__,114,22,68,45
2nd value: (22 x 2)-114= -70
Sequence: __,-70,114,22,68,45
1st value: (114 x 2)- -70= 298. (Subtracting a negative makes the result positive)
Sequence: 298,-70,114,22,68,45
so the order is 298, (-70), 114, 22, 68, 45
ReplyDeleteto start I needed to find the number in between 22 and 45. I reversed the order in finding average by multiplying 45 by 2 which is 90, then subtracted 22 from that which got me 68. I pretty much just repeated that the whole way down. The part where it kind of gets tricky is when the previous number of 22 is 114 which makes the next number down a negative. the equation would be "? + 114 = 44". Since that number was a negative, that means that the next number down, a.k.a the first number, is going to be (114 x 2) - (-70) = 298.
The numbers are 298, -70, 114, 22, 68, and 45. I did the work on paper
ReplyDeleteThe numbers are:
ReplyDelete298, -70, 114, 22, 68 and 45.
I did my work on paper and solved it by starting from the end and moving my way to the front.
WE have __, __, __, 22, __, 45
ReplyDeletebasically i just have to work backwards.
45x2=90
90-22=68
#5=68
__, __, __, 22, 69, 45
now we continue this but now with 68.
68x2=136
136-22=114
#3=114
__, __, 114, 22, 68, 45
22x 2=44
44-114=-70
#2= -70
__, -70, 114, 22, 68, 45
114x2= 128
228-(-70)=298
#1=298
The final sequence is:
298, -70, 114, 22, 68, 45
The list of numbers that we currently have right now is __, __, __, 22, __, 45
ReplyDeleteSo we would have to start at 45, and work our way backwards.
45 * 2 = 90
90 - 22 = 98
Now we know that the fifth number is 68. Check: (22 + 68) / 2 = 45
__, __, __, 22, 68, 45
From here on out, we just take the newest number, and start working with it.
68 * 2 = 136
136 - 22 = 114
__, __, 114, 22, 68, 45
22 * 2 = 44
44 - 114 = -70
__, -70, 114, 22, 68, 45
114 * 2 = 228
228 - -70 = 298
Since that is the last number, we have completed our list!
The final sequence:
298, -70, 114, 22, 68, 45
You can work backwards to get the sequence. 45 * 2 = 90. 90-22 = 68. The fifth number of the sequence is then 68. I can then do 68 * 2 = 136. 136 - 22 is 114. The third number is then 114. I can then multiply 22 by 2 to get 44. Now I have to subtract 114 from 44, which is -70. Now I multiply 114 by 2, which is 228. 228 - (-70) is 298. Therefore the sequence is 298, -70, 114, 22, 68, and 45.
ReplyDeletePOTW
ReplyDeleteThese are the numbers that we know of, and how many we need to figure out..
____, ____, ____, 22, ____, 45
All we have to do is work backwards, using the last number we found. Because we are just starting off, we will use 45.
45*2 = 90
90 - 22 = 68
68 must be the fifth number, since we used 48 to figure it out. To find out the next number, it is the same process except using the number 68. We just keep going like this until we find all the numbers which are...
298, -70, 114, 22, 68, 45
Grade 8 POTW:
ReplyDeleteThe 6 numbers in the sequence are 298,-70,114,22,68,45. I started to work backwards, from the end to the beginning. My work is in my math notebook.
298 -70 114 22 68 45 I had to work backwards, starting with 5 to make it work
ReplyDeletePOTW #12
ReplyDeleteInfo:
- 6 numbers
- Every number after the two is the average of the two numbers
- 4th number is 22 and 6th number is 45
Find: All 6 numbers in the sequence.
Since I was given the last number, I can work backwards.
45 x 2 = 90
90 - 22 = 68
That means the second last number must be 68. To find the rest of the numbers I can do the same:
68 x 2 = 136
136 - 22 = 114
and so on.
Finally I would eventually get all of the numbers which would be:
298, -70, 114, 22, 68, 45
Grade 7 POTW:
ReplyDeleteTo get this, I worked backwards. If you look here it was ?,?,?,22,?,45. We start at 45 and do 45*2=90. Now I I subtract 22 from 90, I get 68. So now we have ?,?,?,22,68,45. Next we go to the fifth number in the sequence. 68*2=136. And 136-22=114, making 114 the 3rd number in the sequence. Now we have ?,?<114,22,68,45. SO we again move back one and we are at the fourth number which is 22. 22*2=44 and 44-114+-70. So now we have ?,-70,22,68,45. Now we go one number back to the third number (114). 114*2=228. 228-(-70)=298, making the first number in the sequence 298. And there we have our completed sequence! 298,-70,114,22,68,45.
POTW:
ReplyDeleteAfter working backwards in order to figure out any averages, I ended up with:
298,-70,114,22,68,45
Work is on paper.
298, -70, 114, 22, 68, 45
ReplyDeleteAn POTW #12
ReplyDeleteSo there are 6 numbers, after every 2 numbers the next would be the average, 4th number is 22, and 6th number is 45
_, _, _, 22, _, 45
45 is the average of 22 and something.
45 x 2 = 90
90 - 22 = 68
_, _, _, 22, 68, 45
68 x 2 = 136
136 - 22 = 114
_, _, 114, 22, 68, 45
22 x 2 = 44
44 - 114 = -70
_, -70, 114, 22, 68, 45
114 x 2 = 228
228 - -70 = 298
All 6 numbers in the sequence are 298, -70, 114, 22, 68, 45
POTW #12
ReplyDeleteSo, we have to find a sequence of 6 numbers. We have two numbers already given. Also, after every 2 numbers, the next number will be their average.
So we'll start with our two given numbers.
45 * 2 = 90
90 - 22 = 68
(We're working backward to find our 6 number sequence)
Now, we'll continue with our strategy to find the next few numbers.
68 * 2 = 136
136 - 22 = 114
22 * 2 = 44
44 - 114 = -70
114 * 2 = 228
228 - (-70) = 298
Eventually, the sequence will end up to be:
298, -70, 114, 22, 68, 45
POTW #12 (I thought I submitted my answer but turns out I didn't):
ReplyDeleteTo start off, we have a line of 6 boxes. The numbers 22 and 45 are already given to us, along with the clue that every number after the first two is the average of the previous two numbers.
Since the 22 and 45 are placed in the second half of the boxes, we can work backwards.
In order to find the average (in this case), you multiply the two numbers and then divide by 2.
Square #5: We already have the numbers 22 and 45. So, (22+x)/2=45
Again, we can work backwards:
45*2=90 90-22=68 Therefore, the number in the fifth square is 68.
Now we use the same strategy of working backwards for the rest.
Square #3: The third square is 114.
(x+22)/2=68 68*2=136 136-22= 114
Square #2: The second square is -70.
(x+114)/2=22 22*2=44 44-114=(-70)
Square #1: The first square is 298.
((-70)+x)/2=114 114*2=228 228-(-70)=298
Therefore, the order of the numbers (from left to right) is 298, -70, 114, 22, 68, 45.