Question

answer each question and round your answer to the nearest tenth.

1. a model house has a scale of 1 in : 2 ft. if the real house is 26 ft wide then how wide is the model house?
2. a 6.5 ft tall car standing next to an adult elephant casts a 33.2 ft shadow. if the adult elephant casts a shadow that is 51.5 ft long then how tall is it?

Explanation:

Question 9

Step1: Understand the scale

The scale is \(1\) in : \(2\) ft, meaning \(1\) inch on the model represents \(2\) feet in real. Let \(x\) be the width of the model house in inches.
We set up a proportion: \(\frac{1\ \text{in}}{2\ \text{ft}}=\frac{x\ \text{in}}{26\ \text{ft}}\)

Step2: Solve the proportion

Cross - multiply: \(2\times x = 1\times26\)
Then \(x=\frac{26}{2}=13\)

Step1: Set up the proportion

Let the height of the elephant be \(h\) feet. Since the ratio of height to shadow length should be the same for the car and the elephant.
For the car: \(\frac{\text{height}}{\text{shadow length}}=\frac{6.5}{33.2}\)
For the elephant: \(\frac{h}{51.5}\)
So we have the proportion \(\frac{6.5}{33.2}=\frac{h}{51.5}\)

Step2: Solve for \(h\)

Cross - multiply: \(33.2\times h=6.5\times51.5\)
First, calculate \(6.5\times51.5 = 334.75\)
Then \(h=\frac{334.75}{33.2}\approx10.1\) (rounded to the nearest tenth)

Answer:

The width of the model house is \(13.0\) inches (rounded to the nearest tenth).

Question 10