Chapter 5.1, Problem 37PS

Solution

To calculate: The number of photos that can be stored in camera when the average photo size is $3.87$ megapixels.

The number of photos that can be stored in camera when the average photo size is $3.87$ megapixels is $27$.

Given information:

The number $n$ of photos that can be stored in digital camera varies inversely with the average size $s$ of the photos. If the digital camera can store $54$ photos when the average photo size is $1.92$ megapixels.

Formula used:

Two variables $x\text{ and }y$ show inverse variation if they are related as below:

  $y=\frac{a}{x}$.

Where, $a$ is a constant.

Explanation:

Let the number of photos that can be stored be $n$ and the average size of each photo be $s$.

Now, as the number of photos that can be stored in the digital camera varies inversely with the average size of a photo, so

  $n=\frac{a}{s}$.

Now, substitute $n=54$ and $s=1.92$ and solve for $a$.

  $\begin{array}{c}54=\frac{a}{1.92}\\ a=103.68\end{array}$

So, $n=\frac{103.68}{s}$.

Now, for $s=3.87$ ,

  $\begin{array}{c}n=\frac{103.68}{3.87}\\ \approx 27\end{array}$

Therefore, the number of photos that can be stored in camera when the average photo size is $3.87$ megapixels is $27$.