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Math Help - I want to know how to set up this equation.

  1. #1
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    Oct 2009
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    I want to know how to set up this equation.

    So say I have to take this medication, I have 9600mg total. I have to take 120mg's every day for the first week. And for each week after that I have to add 40mg more. So it would be 120mg's per day for the first week, 160mg per day for the second week ect.. ect..

    What I want to know is how to set up an algebraic equation that will show me how many days I will be taking this medication for until it is gone.. Now Ive already figured it out in a childish 6th grader manner and I know that the answer is 43 days. This is how I did it:

    9600mg Total

    120mg/day/week, 840mg, week 1

    160mg/day/week, 1120mg, week 2

    200mg/day/week, 1400mg, week 3

    240mg/day/week, 1680mg, week 4

    280mg/day/week, 1960mg, week 5

    320mg/day/week, 2240mg, week 6

    Finally. 360mg for 1 day = 9600mg total.

    6 weeks and 1 day. 43 days.

    I had to figure out for each weak individually but I KNOW there is has to be some kind of equation for this I just have NO idea how to set it up with the sum of how many mg's I have to take changing every week. So if anyone can figure it out that would be awesome.
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  2. #2
    MHF Contributor
    Joined
    Sep 2008
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    West Malaysia
    Posts
    1,261
    Quote Originally Posted by Psymon View Post
    So say I have to take this medication, I have 9600mg total. I have to take 120mg's every day for the first week. And for each week after that I have to add 40mg more. So it would be 120mg's per day for the first week, 160mg per day for the second week ect.. ect..

    What I want to know is how to set up an algebraic equation that will show me how many days I will be taking this medication for until it is gone.. Now Ive already figured it out in a childish 6th grader manner and I know that the answer is 43 days. This is how I did it:

    9600mg Total

    120mg/day/week, 840mg, week 1

    160mg/day/week, 1120mg, week 2

    200mg/day/week, 1400mg, week 3

    240mg/day/week, 1680mg, week 4

    280mg/day/week, 1960mg, week 5

    320mg/day/week, 2240mg, week 6

    Finally. 360mg for 1 day = 9600mg total.

    6 weeks and 1 day. 43 days.

    I had to figure out for each weak individually but I KNOW there is has to be some kind of equation for this I just have NO idea how to set it up with the sum of how many mg's I have to take changing every week. So if anyone can figure it out that would be awesome.
    HI

    notice that this forms a AP

    840 , 1120 , 1400 , ...

    where a=840 and d=280 , Sn=9600

    so 9600=n/2[2(840)+(n-1)(280)]

    You will find that n is 6.1499 .

    That means you need 6.1499 weeks to complete the medication which is approximately 43 days .
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