Question

in a scale model of a boat, 1 inch represents 10 feet.
image of a boat scale 1 in : 10 ft
answer the following.
(a) the height of the real boat is 30 feet. what is the height of the boat in the scale model?
\boxed{} inches
(b) in the scale model, the length of the boat is 8 inches. what is the length of the real boat?
\boxed{} feet

Explanation:

Part (a)

Step1: Understand the scale

The scale is \(1\) inch represents \(10\) feet, so the ratio of model height to real height is \(\frac{1\ \text{inch}}{10\ \text{feet}}\).

Step2: Set up the proportion

Let \(x\) be the model height. We have \(\frac{x}{30\ \text{feet}}=\frac{1\ \text{inch}}{10\ \text{feet}}\).

Step3: Solve for \(x\)

Cross - multiply: \(10x = 30\times1\). Then \(x=\frac{30}{10}=3\).

Step1: Use the scale ratio

The scale is \(1\) inch : \(10\) feet. If the model length is \(8\) inches, let \(y\) be the real length.

Step2: Set up the proportion

\(\frac{1\ \text{inch}}{10\ \text{feet}}=\frac{8\ \text{inches}}{y}\)

Step3: Solve for \(y\)

Cross - multiply: \(y = 8\times10=80\).

Answer:

\(3\)

Part (b)