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Hayyy, this is my process I used to answer this question.
INFO GIVEN: - 1/8 of $1000 Alision - 1/5 of $1000 Bob - Alison + Bob / 2 (mean/average) = Carl - The rest = Dana
First, I had to find how much Alison and Bob receive out of the total of $1000. For Alison's share, she gets of 1/8 of the total. So, I divided 1000 with 8 which gave me $125. That means 1/8 of $1000 is $125. Therefore, Alison will receive $125. Then, I did used the same process for Bob because I'm trying to find 1/5 of $1000. So I divided 1000 into 5 equal parts, this gave me $250. So, Bob will receive $250, because $250 is 1/5 of $1000.
Next, I had to find Carl's share of the money. He got the average of what Alison and Bob received, therefore, I found the mean of Alisons share and Bobs share. Central Tendency - Mean: $125 + $250 = $375 2 / $375 = $187.5 Carl receives $187.50.
Since Dana receives the rest of the money, I added up what Alison got, what Bob got and what Carl got altogether. $375 (A+B) + $187.50 (C) = $562.50 (ALTOGETHER)
Then I subtracted that with the total of $1000. Which gave me $437.50. $1000 (total project money) - $562.50 = $437.50 (D)
Therefore, Dana receives 437.50/1000. WE could reduce that by dividing the numerator and denominator by 10 to make it out of a denominator of 100. 437.50 /10 43.75 _____ ______ 1000 /10 100
So that means it is 44(rounded up) / 100. Which can be reduced by dividing both the numerator and denominator by 4 to equal 11/25. Which is the fractional amount of what Dana will receive.
Thank you for reading my possible solution. - Kajana [ There would be a continuation for the algebraic expression ]
Let x be the total amount ($1000) First, I wanted to make sure I knew how to find the total of everything, so if x=1000, and 1/8 of it is Allison's amount, I could do x/8, or 1000/8, and I could do the same with Bob (x/5, or 1000/5). If Carl is the average amount of Allison and Bob, that means the equation to find it would look something like this: x/8+x/5 ______ (let's pretend the line is one above, the main point is just to divide >.<) 2 If Dana is just the remainder, I don't have to worry about her. XD So, I first found the simplest things out first, which was finding Allison's and Bob's amount, which was just simple division. X/8, or 1000/8 is 125, so Allison receives $125. Bob gets 1/5, or X/5, or 1000/5, which is 200, so Bob makes $200. If I just plug in Allison's and Bob's totals into the equation I made into finding Carl's amount, it's really just (125+200)/2. 125+200=325, and 325/2= 162.5, so Carl made $162.5. Dana is just the remainder of the money, so it's like x- (125+200+162.5)= Dana's amount. So it's like 1000- 487.5, which is 512.5, so Dana made $512.5 WOW Dana did a lot of work if I'm right.....
THIS QUESTION IS TRES SIMPLE. FIRST I CALCULATED 1/5 OF 1000 AND 1/8 OF 1000. 1/5 OF 1000 IS 200 AND 1/8 OF 1000 IS 125. I ADDED THEM TOGETHER. 200+125=325. 325/2=162.5 1000-200-125-162.5=512.5, OR WHAT DANA RECEIVES. DANA RECEIVES $512.50. SHE RECEIVES 51250/100000. SIMPLIFIED, THAT IS 41/80.
Good work everyone, especially the students who were able to use algebraic terms to find their solution. The correct answer was $512.50 or 41/80. If you obtained a different result, do you see why?
My sister and I did this together! :)
ReplyDeleteBefore we did anything, we wanted to create algebraic expressions to help us find the answer. Here they are:
a = 1/8
b = 1/5
c = a+b / 2
d = Total - a+b+c
We first converted the fractions with common denominators.
1/8 and 1/5 = Common denominator of 40
5/40 and 8/40
Since c = a+b , we add 5 and 8
c = 5+8
c = 13
Then we divide it by two (because c is the "average" of what a+b received).
13 / 2 = 6.5
Okay, so far we have:
a = 5
b = 8
c = 6.5
Total is 40. So now we have to subtract a+b+c from 40. What is a+b+c?
a+b+c = 5 + 8 + 6.5
= 19.5
Then we subtract this amount from 40.
40 - 19.5 = 20.5
Therefore, d = 20.5
To find the fractional amount, we divide 20.5 by 40 and multiply it by 100.
20.5 / 40 = 0.5125
0.5 (rounded) x 100 = 50%
Percent -> Fraction = 50/100 or 1/5
This means that d (Dana) receives 1/5 (remainder)
:) Have a great day
- Jonathan and Rachel
Opps. Sorry I meant Dana receives 1/2 (50/100).
DeleteThe fraction of the prize money could also be 20.5 / 40,
Deleteor 41 / 80 (to make the fraction not a decimal)
*not rounded values in this case
Yes! I was going to comment that the original answer is not accurate enough! The fractional amount is 41/80, so not quite half!
DeleteHayyy, this is my process I used to answer this question.
ReplyDeleteINFO GIVEN:
- 1/8 of $1000 Alision
- 1/5 of $1000 Bob
- Alison + Bob / 2 (mean/average) = Carl
- The rest = Dana
First, I had to find how much Alison and Bob receive out of the total of $1000. For Alison's share, she gets of 1/8 of the total. So, I divided 1000 with 8 which gave me $125. That means 1/8 of $1000 is $125. Therefore, Alison will receive $125.
Then, I did used the same process for Bob because I'm trying to find 1/5 of $1000. So I divided 1000 into 5 equal parts, this gave me $250. So, Bob will receive $250, because $250 is 1/5 of $1000.
Next, I had to find Carl's share of the money. He got the average of what Alison and Bob received, therefore, I found the mean of Alisons share and Bobs share.
Central Tendency - Mean:
$125 + $250 = $375
2 / $375 = $187.5
Carl receives $187.50.
Since Dana receives the rest of the money, I added up what Alison got, what Bob got and what Carl got altogether.
$375 (A+B) + $187.50 (C) = $562.50 (ALTOGETHER)
Then I subtracted that with the total of $1000. Which gave me $437.50.
$1000 (total project money) - $562.50 = $437.50 (D)
Therefore, Dana receives 437.50/1000. WE could reduce that by dividing the numerator and denominator by 10 to make it out of a denominator of 100.
437.50 /10 43.75
_____ ______
1000 /10 100
So that means it is 44(rounded up) / 100.
Which can be reduced by dividing both the numerator and denominator by 4 to equal 11/25. Which is the fractional amount of what Dana will receive.
Thank you for reading my possible solution.
- Kajana
[ There would be a continuation for the algebraic expression ]
Let x be the total amount ($1000)
ReplyDeleteFirst, I wanted to make sure I knew how to find the total of everything, so if x=1000, and 1/8 of it is Allison's amount, I could do x/8, or 1000/8, and I could do the same with Bob (x/5, or 1000/5). If Carl is the average amount of Allison and Bob, that means the equation to find it would look something like this:
x/8+x/5
______ (let's pretend the line is one above, the main point is just to divide >.<)
2
If Dana is just the remainder, I don't have to worry about her. XD
So, I first found the simplest things out first, which was finding Allison's and Bob's amount, which was just simple division. X/8, or 1000/8 is 125, so Allison receives $125. Bob gets 1/5, or X/5, or 1000/5, which is 200, so Bob makes $200.
If I just plug in Allison's and Bob's totals into the equation I made into finding Carl's amount, it's really just (125+200)/2. 125+200=325, and 325/2= 162.5, so Carl made $162.5. Dana is just the remainder of the money, so it's like x- (125+200+162.5)= Dana's amount. So it's like 1000- 487.5, which is 512.5, so Dana made $512.5
WOW Dana did a lot of work if I'm right.....
THIS QUESTION IS TRES SIMPLE. FIRST I CALCULATED 1/5 OF 1000 AND 1/8 OF 1000. 1/5 OF 1000 IS 200 AND 1/8 OF 1000 IS 125. I ADDED THEM TOGETHER. 200+125=325. 325/2=162.5 1000-200-125-162.5=512.5, OR WHAT DANA RECEIVES. DANA RECEIVES $512.50. SHE RECEIVES 51250/100000. SIMPLIFIED, THAT IS 41/80.
ReplyDeleteThe post that says the author was "April Du" is actually me -__-
ReplyDeleteI accidentally wrote the post on my sister's account. Sorry about that :(
Good work everyone, especially the students who were able to use algebraic terms to find their solution. The correct answer was $512.50 or 41/80. If you obtained a different result, do you see why?
ReplyDelete