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A person 5'8" tall shrinks to 1' tall. Proportionately how much would her 8' ceiling shrink?

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3 Answers

All proportion problems involve two descriptions in two different ways.

This problem asks for height, and one decription is
           height of person and height of ceiling
another is height before shrinking and height after shrinking.

Once you have determined this, you write a table like this

              first descripton                                            first descripton
                way 1                                                             way 2

second description
way 1

second description
way 2

For your example, that is

height of person                                height of ceiling

height before           68                                                   96

height after             12                                                     c
shriking

From this table you can read off the proportion by placing fraction bars in the same place and an equal sign in between the two fractions. Whether you go across or down doesn't matter. That is you can get either

                            68/12             =                  96/c                      by creating the
                                                                                                  fractions vertically
or
                            68/96             =                  12/c                      by creating the
                                                                                                  fractions horizontally

In fact you can even go from right to left or bottom to top. The important thing is just that you do it the same way in both cases. That is you could also get

                         12/68 = c/96
and
                          96/68 = c/12

Try it out. Solve all four equations for c. You will get the same answer each time. So the most important thing is to set up your table correctly.

 

If you shrink yourself n number of times, you should shrink everything else n number of times to maintain the proportions. It's that simple.

That is,


you are 5'8", which is 68 inches (have to bring everything to a common unit of measure)

your ceiling is 8", which is 96 inches.

Now you shrunk yourself down to 1", which is 12 inches, that is you shunk yourself 68/12= 5.66 times.


Answer,

Proportionately her 8' ceiling would shrink 5.66 times.

Now, if you also want her new ceiling height, the the current ceiling height shoud be divided by the same number of times, which is 96/5.66=17.14. Now that is 17.14 inches heigh. Answer, your ceiling's proportionate height is 17.14 inches.

First off, I want to compliment the fact that you have done much of the work already.  You have clearly shown the parts of the problem that you know how to do and what part of the problem is giving you trouble.  You make the job easier for any teacher or tutor.

Now to address your question...

A proportion is an equation in which two ratios (fractions) are equatl to each other.  The numerator in the fractions represents one value, while the denominator equals another.

In the problem that you are solving, the ratio compares the person's height to the ceilings height

(person's height/ceiling height)

Using p to represent the height of the person and c to represent the height of the ceiling, you would have the ratio p1/c1 = p2/c2.  The subscript 1 (1) represents the original heights, while the subscript 2 (2) represents the new heights.

After substituting in the new values, you should get the proportion
 68/96 = 12/c

Solve the proportion for c to get your final answer.

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