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Math Help - Ratio question

  1. #1
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    Ratio question

    Points A, B, C and D are placed in that order on a line so that AB = 2BC = CD. Express
    BD as a fraction of AD.

    If the radius of a circle is increased by two units, find the ratio of the new circumference to the new diameter.

    There are more but I think if I get the hang of these I will get the rest. Could someone help me to do these
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  2. #2
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    Quote Originally Posted by jgv115 View Post
    Points A, B, C and D are placed in that order on a line so that AB = 2BC = CD. Express
    BD as a fraction of AD.

    If the radius of a circle is increased by two units, find the ratio of the new circumference to the new diameter.

    There are more but I think if I get the hang of these I will get the rest. Could someone help me to do these
    If you label the distances between the points on the line...

    AB=2x
    BC=x
    CD=2x

    \displaystyle\frac{BD}{AD}=\frac{3x}{5x}\Rightarro  w\ BD=\frac{3}{5}AD
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  3. #3
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    Quote Originally Posted by jgv115 View Post

    If the radius of a circle is increased by two units, find the ratio of the new circumference to the new diameter.
    The ratio of the circumference of a circle to it's diameter is \pi

    \displaystyle\frac{{\pi}D}{D}=\frac{2{\pi}R}{2R}=\  pi

    \displaystyle\frac{2{\pi}(R+2)}{2(R+2)}=\pi
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  4. #4
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    Hello, jgv115!

    \text{Points }A, B, C\text{ and }D\text{ are placed in that order on a line}

    \text{so that: }\: AB = 2BC = CD.\;\text{ Express }BD\text{ as a fraction of }AD.

    If you had made a simple sketch, you could "eyeball" Archie's solution.


    . . \begin{array}{cccccccccc}<br />
\bullet & ---- & \bullet & -- & \bullet & ---- & \bullet \\<br />
A & 2x & B & x & C & 2x & D \end{array}




    \text{If the radius of a circle is increased by two units,}
    \text{find the ratio of the new circumference to the new diameter.}

    This is a trick question.

    The ratio of the circumference of any circle to its diameter is \pi.

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  5. #5
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    Thanks so much guys!

    There is one more I found difficulty with:

    If a : b = 3 : 4 and a : (b + c) = 2 : 5, find the ratio a : c.

    How do I do this?
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  6. #6
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    Quote Originally Posted by jgv115 View Post
    Thanks so much guys!

    There is one more I found difficulty with:

    If a : b = 3 : 4 and a : (b + c) = 2 : 5, find the ratio a : c.

    How do I do this?
    A quick way is....

    \displaystyle\frac{a}{b}=\frac{3}{4}\Rightarrow\fr  ac{a}{b}=\frac{6}{8}

    \displaystyle\frac{a}{b+c}=\frac{2}{5}\Rightarrow\  frac{a}{b+c}=\frac{6}{15}

    Therefore the numbers are in the ratio a:b:c=6:8:7

    Hence

    a:c=6:7
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  7. #7
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    Hello, jgv115!

    Another approach . . .


    \text{If }a\!:\! b \,=\, 3\!:\!4\,\text{ and }\,a\!:\!(b + c) \,=\, 2\!:\!5,\,\text{ find the ratio }a\!:\!c.

    We are given: . \begin{Bmatrix} \dfrac{b}{a} &=& \dfrac{4}{3} & [1] \\ \\[-3mm] \dfrac{b+c}{a} &=& \dfrac{5}{2} &  \Rightarrow & \dfrac{b}{a} + \dfrac{c}{a} &=& \dfrac{5}{2} & [2] \end{Bmatrix}


    Substitute [1] into [2]: . \displaystyle \frac{4}{3} + \frac{c}{a} \:=\:\frac{5}{2} \quad\Rightarrow\quad \frac{c}{a} \:=\:\frac{7}{6}


    Therefore: . a\!:\!c \:=\:6\!:\!7

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  8. #8
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    Ahh!! Ok, it seems so easy now

    Thanks for all the help guys!!
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    Alright, I've gotten into questions that has to do with ratio of volumes and areas.

    How would I go about doing this one:

    Three similar jugs have heights 8 cm, 12 cm and 16 cm. If the smallest jug holds 1/2 litre, find the capacities of the other two.
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  10. #10
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    Quote Originally Posted by jgv115 View Post
    Alright, I've gotten into questions that has to do with ratio of volumes and areas.

    How would I go about doing this one:

    Three similar jugs have heights 8 cm, 12 cm and 16 cm. If the smallest jug holds 1/2 litre, find the capacities of the other two.
    If the jugs were "elongated" versions of each other, their volumes would be in the ratio 8:12:16 or 2:3:4

    However, they are "similar", so they also expand in width and depth as the height changes
    such that they are magnified versions of each other.

    12=8+4=1.5(8)

    16=2(8)

    8cm(Wcm)(Dcm)k=0.5\;\;litres

    12cm(1.5Wcm)(1.5Dcm)k=1.5(8cm)1.5(Wcm)1.5(Dcm)k=(0  .5\;\;litres)[1.5]^3

    16cm[2Wcm][2Dcm]k=2(8cm)2(Wcm)2(Dcm)k=(0.5\;\;litres)[2]^3

    \displaystyle\left[\frac{3}{2}\right]^3=\frac{27}{8}

    The volumes are in the ratio 1:\frac{27}{8}:8=8:27:64=2^3:3^3:4^3

    The capacities of the others can then be found.
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