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. the width of the blueprint with the new scale is □ in.

Explanation:

Step1: Find the actual width

Given the original scale \(2\) in. \( = 3\) ft. Let the actual width be \(x\) ft.
We set up a proportion \(\frac{2}{3}=\frac{10}{x}\) (using the ratio of blueprint length to actual length).
Cross - multiply: \(2x = 3\times10\), so \(2x=30\), and \(x = 15\) ft.

Step2: Find the new blueprint width

Now, for the new scale \(4\) in. \(=5\) ft. Let the new blueprint width be \(y\) in.
Set up a proportion \(\frac{4}{5}=\frac{y}{15}\) (using the new scale ratio).
Cross - multiply: \(5y=4\times15\), so \(5y = 60\), and \(y=\frac{60}{5}=12\) in.

Answer:

\(12\)