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Thread: Proportional Expectations: Indiana's and Illinois' comparative death rates

  1. #1

    Proportional Expectations: Indiana's and Illinois' comparative death rates

    Proportional expectations

    Can someone please help me understand how to complete this problem:

    Indiana`s DOT decides to announce a goal to reduce their Motor Vehicle Death rate so that it is proportional to that of Illinois. About how many death would Indiana be able to have to achieve this goal?

    Information for Indiana and Illinois:

    State-MV Deaths-Population-Ratio-Ratio to Scientific Notation-MV per 100,000

    Indiana 693 6,000,000 231:2,000,000 2.31*10^2 2*10^6 11.55
    Illinois 911 12,400,000 911:12,400,000 9.11*10^2 1.24*10^7 7.3468


    What I have tried:

    IL death rate/ IL population = x(expected death rate)/IN population

    9.11*10^2/ 1.24*10^7 = x/2*10^6

    9.11*10^2=911
    1.24*10^7= 12,400,000
    x=x
    2*10^6= 2,000,000

    I realize now that these are the original numbers under ratio so I could have skipped that step, however I am trying to understand the problem.

    911/12,400,000=x/2,000,000

    Cross multiply 12,400,000x=1,822,000,000
    1,822,000,000 divided by 12,400,000
    x=146.94 (rounded) ****This appears to high given the data

    Next I did cross multiplying by keeping it in SN

    9.11*10^2/ 1.24*10^7 = x/2*10^6

    9.11*10^2*2*10^6=18.22*10^8
    x*1.24*10^7= 1.24*10^7x

    Divide

    18.22 by 1.24= 14.69 (rounded)

    Subtract

    10^7-10^8=1

    It appears that the number should be lower than Indiana`s 11.55 per 100,000 people. Am I setting the problem up correctly? I have four more problems that are similar to do so I need to know the steps not just than answer.

    Thanks-Vickie


  2. #2
    Elite Member stapel's Avatar
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    Quote Originally Posted by VickieD View Post
    Proportional expectations

    Can someone please help me understand how to complete this problem:

    Indiana`s DOT decides to announce a goal to reduce their Motor Vehicle Death rate so that it is proportional to that of Illinois. About how many death would Indiana be able to have to achieve this goal?

    Information for Indiana and Illinois:

    State-MV Deaths-Population-Ratio-Ratio to Scientific Notation-MV per 100,000

    Indiana 693 6,000,000 231:2,000,000 2.31*10^2 2*10^6 11.55
    Illinois 911 12,400,000 911:12,400,000 9.11*10^2 1.24*10^7 7.3468

    What I have tried:

    IL death rate/ IL population = x(expected death rate)/IN population

    9.11*10^2/ 1.24*10^7 = x/2*10^6

    9.11*10^2=911
    1.24*10^7= 12,400,000
    x=x
    2*10^6= 2,000,000

    I realize now that these are the original numbers under ratio so I could have skipped that step, however I am trying to understand the problem.

    911/12,400,000=x/2,000,000

    Cross multiply 12,400,000x=1,822,000,000
    1,822,000,000 divided by 12,400,000
    x=146.94 (rounded) ****This appears to high given the data

    Next I did cross multiplying by keeping it in SN

    9.11*10^2/ 1.24*10^7 = x/2*10^6

    9.11*10^2*2*10^6=18.22*10^8
    x*1.24*10^7= 1.24*10^7x

    Divide

    18.22 by 1.24= 14.69 (rounded)

    Subtract

    10^7-10^8=1

    It appears that the number should be lower than Indiana`s 11.55 per 100,000 people. Am I setting the problem up correctly? I have four more problems that are similar to do so I need to know the steps not just than answer.
    I'm not clear on what you're doing, or why...?

    If they're wanting a proportional rate, then aren't they wanting something that equates to the same "per 100,000" amount, multiplied by the number of 100,000's they have in their population...?

  3. #3
    Quote Originally Posted by stapel View Post
    I'm not clear on what you're doing, or why...?

    If they're wanting a proportional rate, then aren't they wanting something that equates to the same "per 100,000" amount, multiplied by the number of 100,000's they have in their population...?


    Thanks for taking the time to reply. Sorry I am so confused with this. The number would be per 100,000. So for every 100,000 there are 11.55 deaths in Indiana.

    The example that I was given in class is:

    State- K-12 Expenditure- Population

    Indiana $9.9 billion 6.5 million
    Illinois $25.6 billion 12.8 million


    IL Expenditures/ IL population = Expected IN expenditures/ IN population

    25.6*10^9/12.8*10^6 = x / 6.5*10^6

    The answer: This means that we could expect Indiana to spend $13 billion on K-12 education if Indiana chose to adopt Illinois spending patterns.

  4. #4
    Elite Member stapel's Avatar
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    Quote Originally Posted by VickieD View Post
    Thanks for taking the time to reply. Sorry I am so confused with this. The number would be per 100,000. So for every 100,000 there are 11.55 deaths in Indiana.

    The example that I was given in class is:

    State- K-12 Expenditure- Population

    Indiana $9.9 billion 6.5 million
    Illinois $25.6 billion 12.8 million


    IL Expenditures/ IL population = Expected IN expenditures/ IN population

    25.6*10^9/12.8*10^6 = x / 6.5*10^6

    The answer: This means that we could expect Indiana to spend $13 billion on K-12 education if Indiana chose to adopt Illinois spending patterns.
    What is the per-100,000 number for Illinois? (Hint: Copy.)

    What then is the value that they want for Indiana? (Hint: No more than the number you just copied.)

    How many 100,000's of population do they have in Indiana? (Hint: Divide.)

    So how many deaths (at most) are they hoping for? (Hint: Multiply.)

    If you are still stuck, please reply showing your work and answers for the above questions. Thank you!

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