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Math Help - quadratic problems

  1. #1
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    quadratic problems

    i need some help with these two quadratic problems:

    - A family drives 240 km to their cottage. They can save fuel by reducing their average speed by 20 km/h and this will mean that the trip will take one hour longer. What is this lower average speed?

    - JB bought some balls for $600. If the cost for each ball had been 25 cents less, she would have had 10 more balls for her $600. How much did she pay for each ball.

    can you help me set up the equation?
    thank you for your expertise
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  2. #2
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    distance=240 km
    let time= x hr
    time speed= 240/x km/hr

    new speed= (240/x)-20 kn/he
    new time= x+1 hr
    but distance is same = 240 km

    so


    240=((240/x)-20))*x+1
    on solving.
    x=3 or -4
    -4 not-possible
    time =3 hr.
    initial speed = 80 km/hr
    new lower speed =(80-20)km/hr=60 km/hr.

    i guess thats the answer?
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  3. #3
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    quadratic problem #1

    thanks so much
    I set up a ratio but it kept coming out wrong
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  4. #4
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    total money= $600
    let no. of balls bought =x
    cost of each ball = $600/x

    new cost = $((600/x)-0.4)
    total money=$600
    no. of balls bught at reduced rate= 600/new cost.
    new number of balls bought=x+10
    so

    x+10= 600/((600/x)-0.4)

    u do the rest.

    and thanks for the thanks.
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  5. #5
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    something went wrong!

    i can see how this makes sense but when I do it, the x works out to 6, which makes them going pretty slow!

    multiplied out:

    240 = 240x/x - 20x + 240/x - 20x
    the x cancels
    240 = 240 - 40x + 240/x

    multiply by x to get rid of denominator
    240x = 240x - 40x^2 + 240x

    combine
    0 = -40x^2 + 240x


    using quadratic formula
    a= -40
    b= 240
    c=0 (can c equal 0?)

    - 240 +- sq root 240^2 - 4*-40*0/ 2(-40)
    - 240 +- 240 / -80
    - 480/ -80
    6

    what did I do wrong?
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  6. #6
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    x is the time taken. so now u will have to calculate speed = d/t

    and c can be zero.
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