Question

think about the process the blueprint of a concrete patio has a scale of 2 in. = 3 ft. you want to find the dimensions of a new blueprint of the patio with a scale of 4 in. = 5 ft. what is the first step in finding the dimensions with the new scale? find the dimensions with the new scale.
what is the first step in finding the dimensions of the new scale?

Explanation:

Step1: Find the actual width

Given the original scale \(2\) in \( = 3\) ft and the original width on the blueprint is \(10\) in.
Let the actual width be \(x\) ft. Using the proportion \(\frac{2}{3}=\frac{10}{x}\). Cross - multiply: \(2x = 3\times10\), so \(x=\frac{3\times10}{2}=15\) ft.

Step2: Find the new width on the blueprint

Now, for the new scale \(4\) in \( = 5\) ft. Let the new width on the blueprint be \(y\) in. Using the proportion \(\frac{4}{5}=\frac{y}{15}\). Cross - multiply: \(5y=4\times15\), then \(y = \frac{4\times15}{5}=12\) in.

Answer:

The first step is to find the actual width (or length if applicable) of the patio using the original scale. If we assume we are only calculating the width (since width is given as \(10\) in in the problem), the new width on the blueprint is \(12\) in.