Q43. - Algebra 1

Question

MOVE THEATERS Use the table at the right.

a. Write a ratio of the number of indoor theaters to the total number of theaters for each year.

b. Do any two of the ratios you wrote for part a form a proportion? If so, explain the realworld meaning of the proportion.

Step-by-Step Solution

Answer

a. For year 2000: $\frac{35567}{36250}$

For year 2001: $\frac{34490}{35173}$

For year 2002: $\frac{35170}{35836}$

For year 2003: $\frac{35361}{35995}$

For year 2004: $\frac{36012}{36652}$

For year 2005: $\frac{37092}{37740}$

For year 2006: $\frac{37776}{38425}$

b. No two ratios form a proportion.

Part a. Step 1. Write down the given data.

The given data is:

Year	Indoor	Drive-In	Total
2000	35567	683	36250
2001	34490	683	35173
2002	35170	666	35836
2003	35361	634	35995
2004	36012	640	36652
2005	37092	648	37740
2006	37776	649	38425

 

Part a. Step 2. Evaluate indoor to total theatre ratio for different years.

For year 2000:

$$\begin{gathered} =\frac{\text{Indoor Theaters}}{\text{Total Theaters}} \\ =\frac{35567}{36250} \end{gathered}$$ 

For year 2001:

$$\begin{gathered} =\frac{\text{Indoor Theaters}}{\text{Total Theaters}} \\ =\frac{34490}{35173} \end{gathered}$$

For year 2002:

$$\begin{gathered} =\frac{\text{Indoor Theaters}}{\text{Total Theaters}} \\ =\frac{35170}{35836} \end{gathered}$$

For year 2003:

$$\begin{gathered} =\frac{\text{Indoor Theaters}}{\text{Total Theaters}} \\ =\frac{35361}{35995} \end{gathered}$$

For year 2004:

$$\begin{gathered} =\frac{\text{Indoor Theaters}}{\text{Total Theaters}} \\ =\frac{36012}{36652} \end{gathered}$$ 

For year 2005:

$$\begin{gathered} =\frac{\text{Indoor Theaters}}{\text{Total Theaters}} \\ =\frac{37092}{37740} \end{gathered}$$

For year 2006:

$$\begin{gathered} =\frac{\text{Indoor Theaters}}{\text{Total Theaters}} \\ =\frac{37776}{38425} \end{gathered}$$ 

Part a. Step 3. Conclusion from the indoor theatre to total theatre ratio.

For year 2000: $\frac{35567}{36250}$

For year 2001: $\frac{34490}{35173}$

For year 2002: $\frac{35170}{35836}$

For year 2003: $\frac{35361}{35995}$

For year 2004: $\frac{36012}{36652}$

For year 2005: $\frac{37092}{37740}$

For year 2006: $\frac{37776}{38425}$

Part b. Step 1. Write down the given statement.

The given data is:

Year	Indoor	Drive-In	Total
2000	35567	683	36250
2001	34490	683	35173
2002	35170	666	35836
2003	35361	634	35995
2004	36012	640	36652
2005	37092	648	37740
2006	37776	649	38425

 

Part b. Step 2. By comparison of indoor to total theatre ratio.

By comparison from sub-part (a), we have

For year 2000: $\frac{35567}{36250}$

For year 2001: $\frac{34490}{35173}$

For year 2002: $\frac{35170}{35836}$

For year 2003: $\frac{35361}{35995}$

For year 2004: $\frac{36012}{36652}$

For year 2005: $\frac{37092}{37740}$

For year 2006: $\frac{37776}{38425}$

Part b. Step 3. By comparison of any two ratios.

Since none of these two ratios are equal, so it is not a proportion.