Question

16. MODELING WITH MATHEMATICS The distance from
the restaurant to the shoe store is the same as the
distance from the café to the florist. The distance from
the shoe store to the movie theater is the same as the
distance from the movie theater to the cafe, and from
the florist to the dry cleaners.
Use the steps below to prove that the
distance from
the restaurant to the movie theater is the same as the
distance from the café to the dry cleaners.
a. State what is given and what is to be proven for
the situation.
b. Write a two-column proof.

Answer 1

Mathematical modelling is the use of mathematical concepts and terminology to model a system

Question a. The given values are;

• a = b
• c = d
• c = e

Where;

a = Distance from the restaurant to the shoe store

b = Distance from the café to the florist

c = Distance from the shoe store to the movie theater

d = Distance from the movie theater to the café

e = Distance from the florist to the dry cleaners

Question b. The two column proof is presented as follows:

$\begin{array}{|l|cl|}\mathbf{Statement}&&\mathbf{Reason}\\a = b&&Given\\c = e&&Given\\a + c = b + e&&Addition \ property \ of \ equality\end{array}$

Where;

a + c = Distance from the restaurant to the movie theater

b + e = Distance from the café to the dry cleaners

The reason the above values and proof are correct are as follows

a. The given parameters are;

Distance from the restaurant to the shoe store, a = Distance from the café to the florist, b

Distance from the shoe store to the movie theater, c = Distance from the movie theater to the café, d

Distance from the shoe store to the movie theater, c = Distance from the florist to the dry cleaners, e

b. Required:

To use steps in a two column proof to prove that the distance from the restaurant to the movie theater = Distance from the café to the dry cleaners

Solution:

Statement  ${}$                                Reason

a = b ${}$                                          Given

c = e ${}$                                          Given

a + c = b + e ${}$                              Addition property of equality

Where;

a + c = Distance from the restaurant to the movie theater

b + e = Distance from the café to the dry cleaners

Therefore;

Distance from the restaurant to the movie theater = Distance from the café to the dry cleaners

Learn more about modelling in mathematics here:

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