Also further below, check out a really interesting video explaining factorials (which was an earlier POTW question). Just click on the picture to start the video. Feel free to write your thoughts in a reply message!
Sunday, March 30, 2014
Math POTW #24 & Cool Factorials Video
This is a patterning question. Most of you are on, or have JUST finished, some questions regarding patterning and algebra. Let's see if you're skills can help you here:
Also further below, check out a really interesting video explaining factorials (which was an earlier POTW question). Just click on the picture to start the video. Feel free to write your thoughts in a reply message!
Also further below, check out a really interesting video explaining factorials (which was an earlier POTW question). Just click on the picture to start the video. Feel free to write your thoughts in a reply message!
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Hello.
ReplyDeleteMy brother and I answered this question. The six numbers are : 298, -70, 114, 22, 68, 45
We grouped the numbers into four groups three (FED, EDC, DCB, CBA , opposite of A,B,C,D,E,F)
Formula / Pattern Rule:
Last number (farthest to the right) x 2 - n (n meaning whatever number is given in the three numbers)
n will then represent the missing number in one of the 4 groups of three
Numbers FED
45 (F) x 2
= 90 - 22
= 68
e = 68
Numbers EDC
68 (E) x 2
= 136 - 22
= 114
c = 114
Numbers DCB
22 (D) x 2
= 44 - 114
= -70
b = -70
Numbers CBA
114 (c) x 2
= 228 - (-70)
= 298
a = 298
Now, all the numbers look like this:
A = 298
B = -70
C = 114
D = 22
E = 68
F = 45
To double-check:
298 + (-70) / 2 = 114 (ABC)
(-70) + 114 / 2 = 22 (BCD)
114 + 22 / 2 = 68 (CDE)
22 + 68 / 2 = 45 (DEF)
And from our background knowledge, the average is the mean (adding all the numbers then substracting by how many numbers are in the set, in this case , 2 )
Thanks
-Jonathan and Rachel
I like how you showed all your work and all your equations.
DeleteHi everyone~
ReplyDeleteSo the order I got was 296, -70, 114, 22, 68, and 45.
I basically just worked backwards the entire time (in a nutshell).
From 45, that's the average of the 2 numbers previous to it, and obviously, if there are 2 numbers, it's x2, so 90. Looking at 90, you know that 22 (one of the 2 numbers to make 90) plus a certain number makes 90, or in averaged terms, 45 (our last number). To find this unknown number, you subtract 22 from 90 (68), and that should be the number in between 22 and 45.
So now we have our next number to work with (68). As usual, the previous 2 numbers added together make twice the next number. So with 68, if you multiply that by 2, you get 136, so you now know that 22+another number=136. 136-22=114, so the number before 22 is 114.
This was the trickiest part, because it dealt with integers, so I started off by looking at my next number: 22. 22x2=44, so 44 is the number 114 and another number have to make. 114 is obviously a lot greater than 44, so I will have to go in the negatives. 44-114= -70, so that's how I got to my next number (-70).
Now I only had one space left, the first one. If the first and second added together equals to twice the amount of the third, I know _+ -70= 228 (114x2). Because I have a number in the negatives, (-70), I know the first number is greater than 228 itself. I know 228- (-70) is 268, which would be my first number.
If I check, 298+ (-70) =228/2=114
-70+114= 44/2=22
114+22=136/68
22+68=90/2=45
And that's how I know I was correct ! :D
This POTW was interesting (as always XD)
Oops sorry I realized I have a typo in my answer...
DeleteIt's 298 in the order, but I wrote it as 296 in the beginning..
Sorry for the confusion!!
Excellent work you three! The order was in fact 298, -70, 114, 22, 68, 45. And great explanations.
ReplyDeleteIf any of your numbers were "off" by a few digits, can you see why?
Well, in my answer, I was off because of a typo haha....
DeleteTO SOLVE DISH KEST E OWN, WE MUST DO DISH:
ReplyDeleteWHAT PLUS 22 DIVIDED BY 2 = 45? WE MUST FIRST DO 45 TIMES 2 TO GET 90, WHICH IS WHAT 22 PLUS ANOTHER NUMBER MUST EQUAL. THEN, WE DO 90-22 TO GET 68, THE 5TH NUMBER. TO SOLVE FOR THE 3RD NUMBER, WE MUST DO THIS:
WHAT PLUS 22 DIVIDED BY 2 EQUALS 68? 68 TIMES 2 EQUALS 136. 136-22=114. THE 3RD NUMBER IS 114.
TO SOLVE FOR THE SECOND NUMBER, WE MUST DO THIS:
WHAT PLUS 114 EQUALS 22? 22 TIMES 2 EQUALS 44. SINCE 114 IS OVER 44, WE DO 114-44 TO GET 70 IN NEGATIVE FORM TO GET THE SECOND NUMBER, -70.
FINALLY, TO GET THE FIRST NUMBER, WE MUST DO THIS:
WHAT PLUS -70 EQUALS 114?
WE DO THIS: 114 TIMES 2= 228. 228 PLUS 70= 298, THE FINAL NUMBER.
298, -70,114 ,22, 68, 45
ReplyDelete