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Math Help - Mixed Questions: Help Needed

  1. #1
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    Mixed Questions: Help Needed

    3 5/8 – ½ =
    1Ύ divided by 2 =

    Write as a ratio in simplest form
    a) 24:40 (would it be 3:5)
    b) 220 cm to 1 m

    Leah and Rachael both drive the same car, and use it basically at the same rate.
    If Leah drives for 8 hours at 60 km/h to visit her best friend, the trip costs $63 in fuel.
    Rachael however drives to see her father but has to drive a further 256 km.
    How much will the trip cost in fuel?

    Three People contribute money to a raffle - $15, $20 and $25. If the winnings are distributed in same ratio as the contributions how much would each person get, if they won $270?
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  2. #2
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    Quote Originally Posted by Quester View Post
    3 5/8 – ½ =
    1Ύ divided by 2 =

    Write as a ratio in simplest form
    a) 24:40 (would it be 3:5)
    b) 220 cm to 1 m
    For the first one convert the mixed numbers into improper fractions:
    3~\frac{5}{8} = \frac{29}{8}

    so
    3~\frac{5}{8} - \frac{1}{2} = \frac{29}{8} - \frac{1}{2}

    = \frac{29}{8} - \frac{4}{8} = \frac{25}{8}

    If you really must have the answer as a mixed number, then
    \frac{25}{8} = 3 + \frac{1}{8} = 3~\frac{1}{8}

    The same thing goes for the other one.

    For the ratios:
    a) 24:40
    \frac{24}{40} = \frac{3 \cdot 8}{5 \cdot 8} = \frac{3}{5}
    and this is 3:5.

    Again, the other one works the same way.

    -Dan
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  3. #3
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    Simplify (expand and collect like terms)
    a)4q + 12q – 3
    b)4 (3a + 1) + 2a
    c)Subtract 3x – 5 from 8x – 18

    Factorise Following
    a)3a + 15 ( is it: 3a + 15 = 3 x a + 3 x 5 = 3(a+5)
    b)4 x – xy + 3x2

    Solve Following

    a)2n + 3 = 17
    b)3x – 4/2 – 6 = 4
    c)5(x – 2) = 4 (x + 9)

    But this particually, I can’t get:

    a) The adjacent sides of a rectangle are (3x – 8) and 6 cm.
    Given that the area of the rectangle is 96 cm^2, find the length of the rectangle and the value of x.

    c)The Three sides of a triangle are 1/1 y + 2 and y = 4. The perimeter is 87 cm. What are the lengths of the three sides?
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  4. #4
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    oh sorry when i wrote 1/2 i mean the fraction 1/2
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  5. #5
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    Quote Originally Posted by Quester View Post
    Simplify (expand and collect like terms)
    a)4q + 12q – 3
    b)4 (3a + 1) + 2a
    c)Subtract 3x – 5 from 8x – 18

    Factorise Following
    a)3a + 15 ( is it: 3a + 15 = 3 x a + 3 x 5 = 3(a+5)
    b)4 x – xy + 3x2

    Solve Following

    a)2n + 3 = 17
    b)3x – 4/2 – 6 = 4
    c)5(x – 2) = 4 (x + 9)

    But this particually, I can’t get:

    a) The adjacent sides of a rectangle are (3x – 8) and 6 cm.
    Given that the area of the rectangle is 96 cm^2, find the length of the rectangle and the value of x.

    c)The Three sides of a triangle are 1/1 y + 2 and y = 4. The perimeter is 87 cm. What are the lengths of the three sides?
    1. Do yourself and do us a favor and start a new thread if you have new questions.

    2. to #1.c.):
    Translate the sentence into a mathematical operation:

    (8x-18)-(3x-5)~\buildrel {expand} \over \longrightarrow~8x-18-3x+5 = 5x-13

    to #2.a.): Yes
    to 2.b.):
    4x - xy + 3x^2= x(4-y+3x)

    to #3.c.):

    5(x-2) = 4 (x + 9)~\iff~ 5x-10=4x+36~\iff~x=46 ....... The last step is: add (-4x+10) on both sides of the equation - you only have to know why this is necessary!

    to #4.a.):
    You are suposed to know that the area of a rectangle is calculated by:

    area = length\ \cdot \ width ....... with
    length = 3x-8 ....... and ....... width = 6

    So you have to solve for x:

    (3x-8) \cdot 6 = 96 ~\iff~ 18x - 48 = 96~\iff~ 18x = 144 ~\iff~ x = \frac{144}{18} = 8

    Therefore the rectangle has the dimensions: l = 16 and w = 6
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  6. #6
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    Quote Originally Posted by earboth View Post
    So you have to solve for x:

    (3x-8) \cdot 6 = 96 ~\iff~ 18x - 48 = 96~\iff~ 18x = 144 ~\iff~ x = \frac{144}{18} = 8

    Therefore the rectangle has the dimensions: l = 16 and w = 6
    how did you get the answer for (3x-8).6 = 96 what does the dot stand for?
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  7. #7
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    Quote Originally Posted by Quester View Post
    how did you get the answer for (3x-8).6 = 96 what does the dot stand for?
    Multiplication
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