Chapter 11.7, Problem 19IP

To determine

To find:How far away should Felicia place projector.

Answer to Problem 19IP

Felicia should place the projector $32$ yards away from the wall.

Explanation of Solution

Given information:

Felicia wants to project a 2-inch by 2-inch slide on to a wall to create an image 128 inches by 128 inches.

Slide projector makes the dimensions of the image twice as large for each yard that is moved away from the wall.

Let $x$ be the number of yards required to create an image that is 128 inches by 128 inches.

Since, each yard doubles the dimensions then multiply it by two from the original and equate it with the desired dimension of $128$ inches.

We get

  $\begin{array}{l}\Rightarrow 2\left(2x\right)=128\\ \Rightarrow 4x=128\\ \Rightarrow \frac{4x}{4}=\frac{128}{4}\\ \Rightarrow x=32\end{array}$

Therefore,

Scale factor $=k=1.5$

Felicia should place the projector $32$ yards away from the wall.