Question

1. a scale drawing of a school bus has a scale of 1/2 inch (in.) to 5 feet (ft.). if the length of the school bus is 4 1/2 in. 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 centimeter (cm) to 80 meters (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 bus

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

Step2: Cross - multiply

$\frac{1}{2}x = 5\times4\frac{1}{2}$. Since $4\frac{1}{2}=\frac{9}{2}$, we have $\frac{1}{2}x=5\times\frac{9}{2}$.

Step3: Solve for $x$

Multiply both sides by 2, $x = 45$ feet.

Step4: Set up proportion for lake

The scale is 1 cm to 80 m. Let $y$ be the width on the drawing for a 1000 - m wide lake. The proportion is $\frac{1\text{ cm}}{80\text{ m}}=\frac{y\text{ cm}}{1000\text{ m}}$.

Step5: Cross - multiply

$80y = 1000$.

Step6: Solve for $y$

$y=\frac{1000}{80}=12.5$ cm.

Answer:

The actual length of the bus is 45 feet. The width of the lake on the scale drawing is 12.5 cm.