Certainly! Let's solve the problem step-by-step:
Step 1: Understand the conversion factor.
The problem states that [tex]\(\frac{18}{6}\)[/tex] inches represents 10 miles. First, simplify [tex]\(\frac{18}{6}\)[/tex]:
[tex]\[
\frac{18}{6} = 3 \text{ inches}
\][/tex]
So, 3 inches represent 10 miles.
Step 2: Calculate the ratio of inches to miles.
We need to find how many miles 1 inch represents. Since 3 inches equal 10 miles, we will divide the number of miles by the number of inches:
[tex]\[
\text{Ratio} = \frac{10 \text{ miles}}{3 \text{ inches}} = \frac{10}{3} \text{ miles per inch}
\][/tex]
Step 3: Determine how many miles 2.25 inches represent.
Now we can use this ratio to find out how many miles are represented by 2.25 inches:
[tex]\[
\text{Miles} = 2.25 \text{ inches} \times \left(\frac{10}{3} \text{ miles per inch}\right)
\][/tex]
Perform the multiplication:
[tex]\[
\text{Miles} = 2.25 \times \frac{10}{3} = 2.25 \times 3.\overline{33} = 2.25 \times 3.3333 \approx 7.5 \text{ miles}
\][/tex]
Step 4: Compare the computed value with given options.
Now, let’s check which option matches our result of 7.5 miles:
- Option (A): [tex]\(\frac{180}{13} \approx 13.846\)[/tex]
- Option (B): [tex]\(\frac{53}{4} = 13.25\)[/tex]
- Option (C): [tex]\(\frac{57}{4} = 14.25\)[/tex]
- Option (D): [tex]\(\frac{27}{2} = 13.5\)[/tex]
- Option (E): 3
None of these options match our computed value of 7.5 miles exactly. Thus, there seems to be no option that exactly represents the 7.5 miles.
