Question

1. two cities are 750 miles apart. if they are 8 inches apart on a map, find the scale. 14. a cell phone tower is 162 ft tall. if a model of the tower is 5 5/8 in. tall, find the scale.

Explanation:

Problem 13

Step1: Convert miles to inches

Since \(1\) mile \( = 5280\) feet and \(1\) foot \(=12\) inches, then \(1\) mile \(=5280\times12 = 63360\) inches.
\(750\) miles \(=750\times63360\) inches.
\(750\times63360=47520000\) inches.

Step2: Find the scale

The scale is the ratio of the map distance to the actual distance.
The map distance is \(8\) inches and the actual distance is \(47520000\) inches.
The scale is \(\frac{8}{47520000}\).
Simplify the fraction: \(\frac{8\div8}{47520000\div8}=\frac{1}{5940000}\).

Step1: Convert feet to inches

Since \(1\) foot \( = 12\) inches, then \(162\) feet \(=162\times12=1944\) inches.

Step2: Convert the mixed - number to an improper fraction

\(5\frac{5}{8}=\frac{5\times8 + 5}{8}=\frac{40+5}{8}=\frac{45}{8}\) inches.

Step3: Find the scale

The scale is the ratio of the model height to the actual height.
The scale is \(\frac{\frac{45}{8}}{1944}\).
Using the rule \(\frac{a}{b}\div c=\frac{a}{b\times c}\), we have \(\frac{45}{8\times1944}\).
\(8\times1944 = 15552\).
Simplify \(\frac{45}{15552}\): \(\frac{45\div9}{15552\div9}=\frac{5}{1728}\)

Answer:

The scale is \(1:5940000\)

Problem 14