Question

A model of a sky scraper is made so that 2 inches represent 50 feet. If the model is 22 inches tall, what’s the height of the actual sky scraper? Show your work. Set up a table like the ones on the exit ticket

Answer 1

We have to calculate the actual height of the skyscrapper.

We know that the scale is such that 2 inches in the model represent 50 ft in the real world.

Then, we can write the scale as:

`k=(M)/(A)=\frac{2\text{ in}}{50\text{ ft}}`

If the model is 22 ft tall, we can find the actual height X as:

`\begin{gathered} k=(M)/(A)=\frac{2\text{ in}}{50\text{ ft}}=\frac{22\text{ in}}{X} \\ \frac{2\text{ in}}{50\text{ ft}}=\frac{22\text{ in}}{X} \\ \frac{50\text{ ft}}{2\text{ in}}=\frac{X}{22\text{ in}} \\ X=\frac{22\text{ in}}{2\text{ in}}\cdot50ft \\ X=11\cdot50ft \\ X=550\text{ ft} \end{gathered}`

Answer: the height of the actual skyscraper is 550 ft.

If we have to construct a table for this problem, we can write:

| Scale | Measurement

Model | 2 in | 50 ft

Skyscrapper | 22 in | 550 ft

were the rows are proportional: 22 in / 2 in = 550 ft / 50 ft