Saturday, March 1, 2014

Math POTW #21 - Use Algebra!

Can you use algebraic variables and expressions to solve this POTW?

9 comments:

  1. My sister and I did this together! :)

    Before 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

    ReplyDelete
    Replies
    1. Opps. Sorry I meant Dana receives 1/2 (50/100).

      Delete
    2. The fraction of the prize money could also be 20.5 / 40,

      or 41 / 80 (to make the fraction not a decimal)

      *not rounded values in this case

      Delete
    3. Yes! I was going to comment that the original answer is not accurate enough! The fractional amount is 41/80, so not quite half!

      Delete
  2. 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 ]

    ReplyDelete
  3. 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.....

    ReplyDelete
  4. 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.

    ReplyDelete
  5. The post that says the author was "April Du" is actually me -__-
    I accidentally wrote the post on my sister's account. Sorry about that :(

    ReplyDelete
  6. 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