Question

a sign shows that the distance to new york is 18 miles. a traveler wants to know what this distance is in kilometers. help the traveler by completing the parts below. (a) let x be the unknown number of kilometers. using the values below, create a proportion that can be used to find x. use the conversion 1 mile = 1.6 kilometers. values: x, 1, 1.6, 18 (b) use the proportion from part (a) to find the distance to new york in kilometers. do not round any computations. kilometers

Explanation:

Part (a)

Step1: Define the proportion

We know that 1 mile is equal to 1.6 kilometers. So, the ratio of miles to kilometers should be consistent. For 18 miles (let the kilometers be \( x \)), the proportion is \(\frac{1}{1.6}=\frac{18}{x}\) (or also \(\frac{x}{18}=\frac{1.6}{1}\) which is equivalent when cross - multiplying). Let's use \(\frac{1}{1.6}=\frac{18}{x}\) (or \(\frac{x}{18}=\frac{1.6}{1}\), both are correct proportion setups based on the conversion factor).

Step2: Verify the proportion

The left - hand side of the proportion \(\frac{1}{1.6}\) represents the conversion factor (1 mile per 1.6 kilometers). The right - hand side \(\frac{18}{x}\) represents 18 miles per \( x \) kilometers. Since the conversion factor should be the same, this proportion holds. Another way is \(\frac{x}{18}=\frac{1.6}{1}\), where the left - hand side is kilometers per mile ( \( x \) kilometers for 18 miles) and the right - hand side is the conversion factor (1.6 kilometers per 1 mile).

Part (b)

Step1: Cross - multiply the proportion

Using the proportion \(\frac{1}{1.6}=\frac{18}{x}\) (from part a), cross - multiplying gives us \(1\times x=1.6\times18\).

Step2: Calculate the value of \( x \)

We know that \(1.6\times18 = 28.8\). So, \(x = 28.8\). If we used the proportion \(\frac{x}{18}=\frac{1.6}{1}\), then \(x=18\times1.6 = 28.8\) directly.

Part (a) Answer:

\(\boldsymbol{\frac{1}{1.6}=\frac{18}{x}}\) (or \(\boldsymbol{\frac{x}{18}=\frac{1.6}{1}}\))

Part (b) Answer:

\(\boldsymbol{28.8}\)

Answer:

Step1: Cross - multiply the proportion

Using the proportion \(\frac{1}{1.6}=\frac{18}{x}\) (from part a), cross - multiplying gives us \(1\times x=1.6\times18\).

Step2: Calculate the value of \( x \)

We know that \(1.6\times18 = 28.8\). So, \(x = 28.8\). If we used the proportion \(\frac{x}{18}=\frac{1.6}{1}\), then \(x=18\times1.6 = 28.8\) directly.

Part (a) Answer:

\(\boldsymbol{\frac{1}{1.6}=\frac{18}{x}}\) (or \(\boldsymbol{\frac{x}{18}=\frac{1.6}{1}}\))

Part (b) Answer:

\(\boldsymbol{28.8}\)