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Math Help - Need help in Ratios

  1. #1
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    Need help in Ratios

    Q#1
    Building hallway is 23.5 inches long.
    The scale is 3.25 inches = 14 feet. How long is the hallway??


    Q#2
    Drawing with a scale of 3.75 inches = 13 feet. What distance on the drawing should be used to represent 9 feet 3 inches??


    Q#3
    On level ground, a street pole casts a shadow 10.7 m long. At the same time, a tree 25.0 m high casts a shadon 35.0 m long. How high is the pole?
    I tried this, but my number is way to small.


    Q#4
    On a map, 8cm = 50 km. What is the distance between the two cities if the distance between them on the map is 13.6cm.
    Actual distance in km??


    Thanks for your help, and explain fully so I can understand.
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    Ratios and multiplying factors

    Hello bradycat
    Quote Originally Posted by bradycat View Post
    Q#1
    Building hallway is 23.5 inches long.
    The scale is 3.25 inches = 14 feet. How long is the hallway??


    Q#2
    Drawing with a scale of 3.75 inches = 13 feet. What distance on the drawing should be used to represent 9 feet 3 inches??


    Q#3
    On level ground, a street pole casts a shadow 10.7 m long. At the same time, a tree 25.0 m high casts a shadon 35.0 m long. How high is the pole?
    I tried this, but my number is way to small.


    Q#4
    On a map, 8cm = 50 km. What is the distance between the two cities if the distance between them on the map is 13.6cm.
    Actual distance in km??


    Thanks for your help, and explain fully so I can understand.
    There are two important things that you need to learn to do when dealing with maps and plans. They are:

    First, in questions like this, change the scale that you've been given so that both bits are in the same units. So, for instance, in #1 the scale you're given is:
    3.25 inches represents 14 feet
    So that's:
    3.25 inches represents 14 \times 12 = 168 inches
    That's a ratio of:
    3.25 : 168
    Noting that 0.25 is one-quarter, multiply both numbers in the ratio by 4 to get rid of decimals. That's:
    3.25 \color{red}\times 4\color{black}:168\color{red}\times 4
    = 13:672
    This means that 13 inches (or feet, or whatever) on the plan represents 672 inches (feet, whatever) on the ground.

    Secondly, learn how to make things bigger and smaller using what are called multiplying factors. It's very simple. If you have a ratio
    A:B
    then the multiplying factors are:
    \frac AB and \frac BA
    That's all. There aren't any more.

    So with the ratio
    13:672
    the multiplying factors are
    \frac{13}{672} and \frac{672}{13}
    And then all you need to know is, to make a number bigger, use the multiplying factor that has the bigger number on top; to make a number smaller use the one that has the smaller number on top.

    OK. Now I'll complete question #1, and see if you can do the others. As we've said, the multiplying factors are:
    \frac{13}{672} and \frac{672}{13}
    On the plan, the hallway is 23.5 inches. Obviously the real hallway is much bigger than this. So we multiply 23.5 inches by \frac{672}{13}. And the answer is:
    23.5\times \frac{672}{13}
    =1215 inches (to the nearest inch)

    = 101 feet 3 inches
    Now have a go at the others. Let us know if you get stuck.

    Grandad
    Last edited by Grandad; March 1st 2010 at 01:14 AM. Reason: Corrected typo
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