Question

1. a scale drawing of a school bus has a scale of 1/2 inch to 5 feet. if the length of the school bus is 4 1/2 inches on the scale drawing, what is the actual length of the bus? explain or show your reasoning.
2. a scale drawing of a lake has a scale of 1 cm to 80 m. if the actual width of the lake is 1,000 m, what is the width of the lake on the scale drawing? explain or show your reasoning.

Explanation:

Step1: Set up proportion for school - bus problem

The scale is $\frac{1}{2}$ inch to 5 feet. Let $x$ be the actual length. The proportion is $\frac{\frac{1}{2}\text{ inch}}{5\text{ feet}}=\frac{4\text{ inches}}{x\text{ feet}}$.

Step2: Cross - multiply

Cross - multiplying gives $\frac{1}{2}x = 4\times5$.

Step3: Solve for $x$

We have $\frac{1}{2}x=20$, then $x = 40$ feet.

Step4: Set up proportion for lake problem

The scale is 1 cm to 80 m. Let $y$ be the width on the scale drawing. The proportion is $\frac{1\text{ cm}}{80\text{ m}}=\frac{y\text{ cm}}{1600\text{ m}}$.

Step5: Cross - multiply

Cross - multiplying gives $80y=1600$.

Step6: Solve for $y$

Dividing both sides by 80, we get $y = 20$ cm.

Answer:

1. The actual length of the bus is 40 feet.
2. The width of the lake on the scale drawing is 20 cm.