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Math Help - direct and inverse variations

  1. #1
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    Question direct and inverse variations

    a) The amount of money that a salesperson makes varies directly as the total amount of sales made. If the salesperson receives $7,500 for selling a hous for $120,000, how much will he or she make if he or she sells a house for $150,000?


    b) If y varies inversely as x^2, and y = 2 when x = 4, what is the constant of variation?


    I'm so confused with these problems. Please explain this to me as best as you can. Thanks!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    i think you meant to say: "The amount of money that a salesperson makes varies directly as the total amount of money made from sales" otherwise the question makes no sense, since you did not tell us how many sales were made, you just told us the value of a single sale. so i will assume the question is to be done as i described above.

    Now, we say two numbers x and y vary directly or are directly proportional if there is a constant k, such that:

    x = k*y

    we say two numbers x and y vary indirectly, or inversly or are inversly proportional if there is a constant k, such that:

    x = k*(1/y) = k/y

    k is called the constant of variation or the constant of proportionality

    Quote Originally Posted by poeticprincess View Post
    a) The amount of money that a salesperson makes varies directly as the total amount of sales made. If the salesperson receives $7,500 for selling a hous for $120,000, how much will he or she make if he or she sells a house for $150,000?
    let x be the amount of money the salesperson makes
    let y be the total amount of money made on a sale, then we have

    x = k*y

    when x = 7500, y = 120000, so
    7500 = 120000k
    => k = 7500/120000 = 1/16
    so our constant of proportionality is 1/16

    how much will he or she make if he or she sells a house for $150,000? well, we simply need to find x when y = 150000

    now x = (1/16)y
    => x = (1/16)(150000)
    => x = 9375

    so the salesperson makes $9375

    b) If y varies inversely as x^2, and y = 2 when x = 4, what is the constant of variation?
    since y varies inversly to x^2, we have

    y = k/(x^2)
    => k = y(x^2)
    when y = 2, x = 4
    => k = 2(4^2)
    => k = 32
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  3. #3
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    Thankies Jhevon!
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