This blog is the online extension of our intermediate classrooms. Our goal is to enhance and document our learning experience throughout the school year, and share this journey with teachers, parents and students. We welcome your constructive feedback, and we look forward to learning with you!
I did this problem in my math notebook and got the answers of 1. Bea's overall average is 72 2. The average of Bea's first and sixth marks is equal to 73 :)
Let's begin: 1st and 2nd. Now (71 + 75)/2=73 Relatively close to the 71 we need. We bring the second number lower by 2. (71 + 73)/2= 72. Let's lower both of them by 1 now... (70+72)= 142/2=71 So we got our first potential two numbers. 1=70 2=72 The third number would equal 150-72= 78 1=70 2=72 3=78 The fourth would be 132-78=54 1=70 2=72 3=78 4=54 The fifth number would have to be 136-54=82 1=70 2=72 3=78 4=54 5=82 And last but not least, the sixth number would be 164-82=82 So in the end the marks Bea Student got is 1=70 2=72 3=78 4=54 5=82 6=82
a) (82+82+70+72+54+78)/6=73 Bea's Average is 73% b) The first average between the first and sixth marks is 76. (82+70)/2=76
Also I like the pun. It's very MEANingful. And I just turned on punny MODE... Ba dum tss (Get it because mean and mode are part of the types of average?)
POTW #31: Strategy: Mess around with the averages.
Solving: Let x be the average of first and sixth marks 71*2+66*2+82*2 = (71+75+66+68+82+x)*2/2 142+132+164 = 362 + x 438 = 362 + x Subtract 362 on both sides x = 76. Basically, this means that I solved b first, which is that the average of the first and sixth mark is 76%.
Part a: All I have to do is add up all of the averages, multiply by two to get all the values(Because the average is only half of the actual two percentages) then divide by 2(Since I counted each value twice; first and second, second and third, third and fourth, and so forth), then divide by 6, since there are 6 numbers and I am finding the average. This would be:
(76+75+66+68+82+76) * 2 / 2 / 6 = 443 / 6 = 73% The average of the six marks / the overall average is 73%.
P.S. In the steps I did, I skipped *2/2 because I basically just cancel them out since they are the exact same, skipping a step.
Alan's Second way of doing the problem: Yeah... The algebra way is so confusing that I'm the only one that probably understands how it works, so here is another way of doing the problem and how I used it to double check!
Step one: For the average of first and second marks, literally use the number. Both the first mark and second mark can be 71. This really doesn't matter, since no matter what those numbers are, the other number would just average it out. Step two: SOLVE! 71 71 79 53 83 81 This is one possibility, but since they are not asking for what the marks actually are, there are multiple answers.
Average would be those numbers added up, divided by 6, giving you 73% as well. First and sixth average would be 71+81 = 152 152/2 = 76%. Same answers proved that my algebra way worked. -Alan
a)
ReplyDeletefirst mark: 65%
second mark: 77%
third mark: 73%
fourth mark: 59%
fifth mark: 77%
sixth mark: 87%
average = sum of numbers / amount of numbers
numbers are 65, 77, 73, 59, 77, 87.
there are 6 numbers
65 + 77 + 73 + 59 + 77 + 87 /6
= 438 /6
= 73
Bea's overall average is 73%
b)
average = sum of numbers / amount of numbers
numbers are 87 and 65.
there are 2 numbers
87 + 65 /2
= 152 /2
= 76
The average of Bea's first and sixth marks is 76%
I did this problem in my math notebook and got the answers of
ReplyDelete1. Bea's overall average is 72
2. The average of Bea's first and sixth marks is equal to 73
:)
Okay so, we first begin off that her first and second marks have to equal to 142.
ReplyDeleteMarks:
1 + 2 = 142
2 + 3= 150
3 + 4= 132
4 + 5= 136
5 + 6= 164
Let's begin:
1st and 2nd. Now (71 + 75)/2=73 Relatively close to the 71 we need. We bring the second number lower by 2. (71 + 73)/2= 72. Let's lower both of them by 1 now...
(70+72)= 142/2=71 So we got our first potential two numbers.
1=70
2=72
The third number would equal 150-72= 78
1=70
2=72
3=78
The fourth would be 132-78=54
1=70
2=72
3=78
4=54
The fifth number would have to be 136-54=82
1=70
2=72
3=78
4=54
5=82
And last but not least, the sixth number would be 164-82=82
So in the end the marks Bea Student got is
1=70
2=72
3=78
4=54
5=82
6=82
a) (82+82+70+72+54+78)/6=73
Bea's Average is 73%
b) The first average between the first and sixth marks is 76.
(82+70)/2=76
Also I like the pun. It's very MEANingful. And I just turned on punny MODE...
Ba dum tss (Get it because mean and mode are part of the types of average?)
Bea's average mark with all of her grades is 73%. The average of her 1st and 6th mark is 76. I did it on the white board.
ReplyDeletePOTW #31:
ReplyDeleteStrategy: Mess around with the averages.
Solving:
Let x be the average of first and sixth marks
71*2+66*2+82*2 = (71+75+66+68+82+x)*2/2
142+132+164 = 362 + x
438 = 362 + x
Subtract 362 on both sides
x = 76.
Basically, this means that I solved b first, which is that the average of the first and sixth mark is 76%.
Part a:
All I have to do is add up all of the averages, multiply by two to get all the values(Because the average is only half of the actual two percentages) then divide by 2(Since I counted each value twice; first and second, second and third, third and fourth, and so forth), then divide by 6, since there are 6 numbers and I am finding the average. This would be:
(76+75+66+68+82+76) * 2 / 2 / 6
= 443 / 6
= 73%
The average of the six marks / the overall average is 73%.
P.S.
In the steps I did, I skipped *2/2 because I basically just cancel them out since they are the exact same, skipping a step.
-Alan-
Alan's Second way of doing the problem:
ReplyDeleteYeah... The algebra way is so confusing that I'm the only one that probably understands how it works, so here is another way of doing the problem and how I used it to double check!
Step one: For the average of first and second marks, literally use the number.
Both the first mark and second mark can be 71. This really doesn't matter, since no matter what those numbers are, the other number would just average it out.
Step two: SOLVE!
71 71 79 53 83 81
This is one possibility, but since they are not asking for what the marks actually are, there are multiple answers.
Average would be those numbers added up, divided by 6, giving you 73% as well.
First and sixth average would be 71+81 = 152
152/2 = 76%.
Same answers proved that my algebra way worked.
-Alan
I did the problem in my head (and with a calculator)
ReplyDeleteBea's overall average is 73, and the average of the first and sixth numbers is 76
Rounding down, Bea's average would be about 72%. Work is similar to other methods above
ReplyDeleteGrade 7 POTW:
ReplyDeletea) she has an overall average of 73%
b) the average of her first and sixth average is 76%
Done in book.
Bea's total average: 73%
ReplyDeleteBea's first and sixth average: 76%
Average=73
ReplyDeleteAverage of 1st and 2nd=76
I think there are so many combinations for doing this?
-Seayrohn
But would the order ("combinations" as you say) really matter Seayrohn?
Deletenot really
Deleteif the combinations makes sense
Deletemy mistake I meant "average of 1st and 6th=76
DeleteBea's total avergae is 73%
ReplyDeleteBea's First and sixth mark average is 76%